UBC Wiki - User contributions [en]

Course:MATH110/Archive/2010-2011/003/Groups/Group 18

2010-11-12T05:29:18Z

RolandWill: /* Homework due October 20th, 2010 */

{{Infobox MATH110 Groups
| group number = 18
| member 1 = [[User:ChouJuChen|Audrey Chen]]
| member 2 = [[User:SifatHasan|Sifat Hasan]]
| member 3 = [[User:CaitlinLastiwkaFarquharson|Caitlin Lastiwka-Farquharson]]
| member 4 = [[User:VictoriaWall|Victoria Wall]]
| member 5 = [[User:RolandWill|Roland Will]]
| member 6 =
}}

==Sub-Pages==

Basic Skills Project [http://wiki.ubc.ca/Course:MATH110/003/Groups/Group_18/Basic_Skills_Project]

==Homework due October 20th, 2010==

I created a page for our homework due tomorrow: [http://wiki.ubc.ca/Course:MATH110/003/Groups/Group_18/Homework_October_20th,_2010 http://wiki.ubc.ca/Course:MATH110/003/Groups/Group 18/Homework October 20th, 2010]

-Roland

I've moved the page, it was missing the ''Course:'' part which means it was created directly inside the wiki and not as a subpage of your group page, which is something the wiki admins don't like that much. By the way, you're allowed to use spaces in the name of your pages.

-- [[User:DavidKohler|DavidKohler]] 06:28, 20 October 2010 (UTC)

==First Group Wiki Homework==

1-5

Victoria Wall

1.A bus traveled from the terminal to the airport at an average speed of 30 mi/hr and the trip took an hour and 20 min. The bus then traveled from the airport back to the terminal and again averaged 30 mi/hr. However, the return trip required 80 min. Explain.

' 'Lets call the terminal T and the airport A. If the bus travelled from T to A at 30mi/hr and it took them one hour and 20 mins to get from T to A at this speed, and there are 60 minutes in one hour, it took the bus 60min + 20min to get to A which is a total of 80min. The bus took 80 min to get from T to A. To get from A to T at the same speed (30mi/hr) it took the bus 80min. 80min = 80 min. This means going from A to T or vis versa at 30 mi/hr it will take the bus 80min.

2.A lady did not have her driver's license with her when she failed to stop at a stop sign and then went three blocks down a one-way street the wrong way. A policeman saw her, but he did not stop her. Explain.

' 'The lady was walking. It never says she was driving.

3.One of three boxes contains apples, another box contains oranges, and another box contains a mixture of apples and oranges. The boxes are labeled APPLES, ORANGES and APPLES AND ORANGES, but each label is incorrect. Can you select one fruit from only one box and determine the correct labels? Explain.

' 'if you selecet from the box APPLES AND ORANGES then you will be able to see the labels if they are correct or not.

4.I am the brother of the blind fiddler, but brothers I have none. How can this be?

' 'Since it says that he is the brother of the blind fiddler it does not mean that the fiddle is male, since he has no brothers than the fiddler must be a female.

5.Two quarters rest next to each other on a table. One coin is held fixed while the second coin is rolled around the edge of the first coin with no slipping. When the moving coin returns to its original position, how many times has it revolved?

' 'This is because the moving quarters revolves two full revolutions

6-10

Caitlin Lastiwka- Farquharson

6. Three kinds of apples are all mixed up in a basket. How many apples must you draw without (without looking) from the basket to be sure of getting at least two of a kind?

' ' To be sure you are getting at least two of a kind, you must select all of the other types of apples, plus two more. Meaning that only once you have selected all of the other apples can you be sure that you will select two of the kind you desire. It can be written like this: x,a x2, b and x3, c, with x representing the quantity of apples. This can be calculated by x2 + x3 +2. X2 representing one of the types of apples, x3 representing the other type and 2 representing 2 of the kind of apples you are trying to select. This is the only way to be sure you are getting at least two of a kind. ' '

7. Suppose you have 40 blue socks and 40 brown socks in a drawer. How many socks must you take from the drawer (without looking) to be sure of getting (i) a pair of the same colour, and (ii) a pair with different colors.

' 'You must take three socks from the drawer to ensure you have a pair that match. This is because if you only select two, one could be brown and one could be blue. Selecting three, ensures that at least two of them will be the same colour. As for part two, you would need to select 41 socks to ensure you had a pair of different coloured socks because if you select 40 or less you could get all the same colour, but selecting 41 ensures you will have at least one pair of mixed colour. ' '

8. Rueben says "Two days ago I was 20 years old. Later next year I will be 23 years old." Explain how this is possible.

' 'It is possible if your birthday is on the 31st of December and today is the 1st of January. This is because on the 30th of December (two days ago) you we’re 20 years old and now you are 21, later this year you will turn 22 on the 31st of December, and therefore 23 the next year.' '

9. A rope ladder hanging over the side of a boat has rungs one foot apart. Ten rungs are showing. If the tide rises five feet, how many rungs will be showing?

' ' 5 rungs will be showing, because if there are 10 showing now, and they are each a foot apart, then for 5 more rungs to be showing there would need to be an increase in the level of water by 5 feet. ' '

10.Suppose one-half of all people are chocolate eaters and one-half of all people are women. (i) Does it follow that one-fourth of all people are women chocolate eaters? (ii) Does it follow that one-half of all men are chocolate eaters? Explain.

' ' No, it does not follow that one-fourth of all people are women chocolate eaters and it does not follow that half of all men are chocolate eaters because are completely independent scenarios. Meaning that the the amount of women there are does not influence the amount of men that will eat chocolate. For example, If 50% of people are women and 50% of the entire population including men and women eat chocolate (arrived at by using the same logic that if 1/4 of women eat chocolate and 1/4 of men eat chocolate), that entire 50% could be comprised of women, meaning that no men eat chocolate disproving the statement.

11-14

Sifat Hasan

11. A woman, her older brother, her son, and her daughter are chess players. The worst player’s twin, who is one of the four players, and the best player are of opposite sex. The worst player and the best player have the same age. If this is possible, who is the worst player?

The four players (according to age, from oldest to youngest) are: woman's older brother, woman, and the son and the daughter (of the same age). Assuming that the children are of the same age (i.e. twins), the worst player is one of them, since they are the only ones who can have a twin. Assuming that the worst player is the daughter, her brother the son, is of the opposite sex as the woman, therefore the woman is the worst player. However, since the worst and the best player are of the same age, this is not possible, because the twins are of the opposite sex and they are of different genders.

12 A Manhattan fellow had a girlfriend in the Bronx and a girlfriend in Brooklyn. He decided which girlfriend to visit by arriving randomly at the train station and taking the first of the Bronx or Brooklyn trains that arrived. The trains to Brooklyn and the Bronx each arrived regularly every 10 minutes. Not long after he began his scheme the man's Bronx girlfriend left him because he rarely visited. Give a (logical) explanation

Assuming that the Bronx and the Brooklyn train arrive one after the other every 10 minutes, the only logical explanation would be that the man in Manhattan coincidentally went to the station 10 minutes or less before a train to Brooklyn arrived, most of the time.

13 If a clock takes 5 seconds to strike 5:00 (with 5 equally spaced chimes), how long does it take to strike 10:00 (with 10 equally spaced chimes)?

If it takes 5 seconds to strike 5, there will be 4 little halts in the middle. Therefore it takes 5 chimes 4 (5/4) = 1.25 second halts to finish. For 10 chimes, there are 9 halts so, it takes 9x 1.25 = 11.25 seconds for 10 halts.

14 One day in the maternity ward, the name tags for four girl babies became mixed up. (i) In how many different ways could two of the babies be tagged correctly and two of the babies be tagged incorrectly? (ii) In how many different ways could three of the babies be tagged correctly and one baby be tagged incorrectly?

(i)and (ii) If we take the babies names as A,B,C and D. There are 6 different combinations of the mix up, that two babies' names can be correct and 2 can be wrong. Assuming the name tags for the babies A,B,C and D are in respective order, they are ABDC, ADCB, ACBD, DBCA, CBAD and BACD. All other combinations for example BCAD will have one correct and 3 incorrect, or all four of them correct, because if 3 are correct, the fourth one has to be correct.

15-16

Roland Will

15. Alex says to you, “I'll bet you any amount of money that if I shuffle this deck of cards, there will always be as many red cards in the first half of the deck as there are black cards in the second half of the deck.” Should you accept his bet?

Answer: No, you shouldn't assuming the deck has equal amounts of red and black cards as in a standard 52 card deck.
Solution: In a standard 52 card deck, half of the cards (26) are black and half are red. If you take 26 cards at random from the deck, x of them will be black and y of them will be red, and x+y=26. As there are 26 of each color in the deck, then x+?=26 for the black cards in the deck and ?+y=26 for the red cards in the deck. As x+y=26 in the first randomly selected 26 cards, then the value of black cards in the other half of the deck must equal y, and the value of red cards in the other half of the deck must equal x meaning that "there will always be as many red cards in the first half of the deck as there are black cards in the second half of the deck."

16. Suppose that each daughter in your family has the same number of brothers as she has sisters, and each son in your family has twice as many sisters as he has brothers. How many sons and daughters are in the family?

Answer:3 total, 2 sister and 1 brother
Solution: Since the daughters in the family each have as many brothers as sisters the amount of sisters, with x standing for the amount of brothers, is x+1. As each brother has twice as many sisters as brothers, the amount of sisters must equal 2(x-1) or 2x-2. To find the number of brother: x+1=2x+1, 1=x-2, 3=x, which means that their are 3 brothers and 4 sisters (x+1= the number of sisters and x=3). This makes sense because a sister would have an equal amount of brothers to sisters, 3 sisters and 3 brothers, if there were 4 sisters and 3 brothers total, and each brother would have 4 sisters and 3 brothers, which is twice the amount of brothers to sisters.

17~21

Audrey Chen

17.The zero point on a bathroom scale is set incorrectly, but otherwise the scale is accurate. It shows 60 kg when Dan stands on the scale, 50 kg when Sarah stands on the scale, but 105 kg when Dan and Sarah both stand on the scale. Does the scale read too high or too low? Explain.

''The scale read too low, since Dan is shown as 60kg and Sarah is 50kg, suppose 60+50=110, 105-110=-5, so that means the scale is smaller than 0 in the beginning''

18. Alice takes one-third of the pennies from a large jar. Then Bret takes one-third of the remaining pennies from the jar. Finally, Carla takes one-third of the remaining pennies from the jar, leaving 40 pennies in the jar. How many pennies were in the jar at the start?

''If the total pennies is "x", Alice take 1/3x, so it has 2/3x left after Alice took it, than Bret take 1/3 out, after Alice took it, which is 2/3x*1/3= 2/9x, so in the beginning they have x, after Alice took it, it has 2/3x left, and Bret took 2/9x, so after Bret took it, it becomes 2/3x-2/9x= 4/9x-2/9x=2/9x left in the jar. Than Carla take 1/3 of the rest, so she took 1/3 of rest which is 2/9x*1/3=3/27x, so Alice took 1/3x, Bret tool 2/9x, Carla took 3/27x, three of them totaly took 1/3x+2/9x+3/27x=18/27x, so there still has x-18/27x= 9/27x= 1/3 left, 1/3x=40pennies, so x=120 pennies, so it was having 120 pennies in the jar.

19. One morning each member of Angela's family drank an eight-ounce cup of coffee and milk, with the (nonzero) amounts of coffee and milk varying from cup to cup. Angela drank a quarter of the total amount of milk and a sixth of the total amount of coffee. What is the least number of people in the family?

''If we let total milk is x, total coffee is y. Than 1/4x+1/6y=8, and because every cup is 8ounce, x+y is multiple by 8. So make it easier, we use 1/4x+1/6y=8 * 12 to both sides. than we will got 3x+2y=96, now we have 3x+2y=96 and x+y is multiple of 8, and the number that multiple by 8 is 8, 16, 24, 32... so 2x+2y= 16, 32, 48, 64, 80, 96, since 3x+2y=96, it can't be more than 96. It will only have 6 possible number, so if you take 3x+2y=96 substracting 2x+2y=16, 32, 48, 64, 80, 96 you can get 6 possible x, which are 80, 64, 48, 32, 16, and 0. Than put the number into 3x+2y=96, if you put 80 in, will get 20, which is bigger than 8, and also 64, 48. If we use 32, it will equal to 8, but that means we have 0 coffee, but coffee can't be 0, so there's only 16 and 0 left. Since Angela had 1/4 of total amount of milk, milk can't be 0. So we got 16ounce than 16*(1/4)=4, so that means she had 8-4=4 's coffee. So 4=1/6 coffee, than the total amount of coffee would be 4*6=24. than x=16 and y=24, 16+24=40 40/8ounce=5, so at least have 5 cups of drinks, so that means at least they have 5 members in Angela's family.''

20.Of two clocks next to each other, one runs 5 min per hour fast and the other runs 5 min per hour slow. At midnight the clocks show the same time. At what time are they are one hour apart?

''Since one clock runs 5 min faster per hour, the other is 5 min slower, after clock runs an hour, two clocks will have 10 min different from each other. 60 min an hour. 60/10=6, so after 6 hours two clocks will having one hour apart, and that would be 6AM.''

21.Sven placed exactly in the middle among all runners in a race. Dan was slower than Sven, in 10th place, and Lars was in 16th place. How many runners were in the race?

''There were 17 runners. Since lars was in 16th place, the runners at least have to be 16, than if Sven is placed exactly in the middle, it means it would have even number of runners. Because Dan is slower and he was at 10 place that tells us Seven has to be before 10th, and if there has 19 runners, Sven and Dan would be at the same place, so it should be 17 runners, than Sven would be at exactly in the middle which at 9th place.''

22-25

Roland Will

22. During a vacation, it rained on 13 days, but when it rained in the morning, the afternoon was sunny, and every rainy afternoon was preceded by a sunny morning. There were 11 sunny mornings and 12 sunny afternoons. How long was the vacation?

Answer: 18 days of vacation.

Solution: 13 of the days of vacation were half sunny and half rainy. As there were 23 sunny mornings and afternoons (11 sunny mornings+12 sunny afternoons = 23 sunny mornings and afternoons), 13 of those sunny afternoons or mornings were on half rainy days. This means there are 10 sunny half-days left over, which equal 5 sunny full days. The 5 sunny full days plus the 13 half sunny/rainy days equal 18 total days of vacation.

23. Suppose you overhear the following conversation: Paul: How old are your three children? Paula: The product of their ages is 36 and the sum of their ages is the same as today's date. Paul: That is not enough information. Paula: The oldest child also has red hair. If you were Paul could you determine the ages of Paula's children? Explain.

Answer: If I were Paul this might be possible, but since we don’t know the date that Paula said this, it is not possible for us to find out.

Solution: There are many different combinations of three numbers that can be multiplied and will produce 36. As we do not know the date that Paula said this, the only thing we can be sure of is that the sum of the ages is less than 31 because no month has more than 31 days. Unfortunately, only one set of ages (ages 1 year old, 1 year old and 36 years old) has a sum greater than 31, which leaves many possible combinations open as possible. For today’s date, the 13th, ages of 2, 2, and 9 would produce 36 and have a sum of 13, but, again, it is uncertain. If it were the first of the month, there would be no possible combinations that would produce 36 and sum 1.

24. Two candles of equal length were lit at the same time. One candle took 6 hr to burn out and the other candle took 3 hr to burn out. After how much time was one candle exactly twice as long as the other candle?

Answer: 2 hours.

Solution: The faster burning candle took half the time to burn as the slower burning candle (3 hours/ 6 hours = 1/2), meaning it burned twice as fast. This means that after 2/3 of the total burning time for the faster burning candle it will be 1/3 of its original height and at the slower burning candle will be at 2/3 of its original height and 1/3 is half of 2/3. Since the faster burning candle took 3 hours to burn, 2/3 of its total burning time is 2 hours.

25. Two candles of length L and L + 1 were lit at 6:00 and 4:30, respectively. At 8:30 they had the same length. The longer candle died at 10:30 and the shorter candle died at 10:00. Find L.

Answer: L=2.

Solution: The shorter candle lasted for 4 hours and the longer candle lasted for 6 hours. As 6 hours – 4 hours = 2 hours and 2 hours / 4 hours = 1/2, the longer candle lasted 50% longer and was, therefore, 50% longer in length. This means that the +1 in L+1 on the longer candle was 1/2 of L. 1/2L=1, so L=2*1, L=2.

Course:MATH110/Archive/2010-2011/003/Groups/Group 18

2010-11-12T05:28:09Z

RolandWill: /* 22-25 */

{{Infobox MATH110 Groups
| group number = 18
| member 1 = [[User:ChouJuChen|Audrey Chen]]
| member 2 = [[User:SifatHasan|Sifat Hasan]]
| member 3 = [[User:CaitlinLastiwkaFarquharson|Caitlin Lastiwka-Farquharson]]
| member 4 = [[User:VictoriaWall|Victoria Wall]]
| member 5 = [[User:RolandWill|Roland Will]]
| member 6 =
}}

==Sub-Pages==

Basic Skills Project [http://wiki.ubc.ca/Course:MATH110/003/Groups/Group_18/Basic_Skills_Project]

==Homework due October 20th, 2010==

I created a page for our homework due tomorrow: [http://wiki.ubc.ca/Course:MATH110/003/Groups/Group_18/Homework_October_20th,_2010 http://wiki.ubc.ca/Course:MATH110/003/Groups/Group 18/Homework October 20th, 2010]

-Roland

I've moved the page, it was missing the ''Course:'' part which means it was created directly inside the wiki and not as a subpage of your group page, which is something the wiki admins don't like that much. By the way, you're allowed to use spaces in the name of your pages.

-- [[User:DavidKohler|DavidKohler]] 06:28, 20 October 2010 (UTC)

1-5

Victoria Wall

1.A bus traveled from the terminal to the airport at an average speed of 30 mi/hr and the trip took an hour and 20 min. The bus then traveled from the airport back to the terminal and again averaged 30 mi/hr. However, the return trip required 80 min. Explain.

' 'Lets call the terminal T and the airport A. If the bus travelled from T to A at 30mi/hr and it took them one hour and 20 mins to get from T to A at this speed, and there are 60 minutes in one hour, it took the bus 60min + 20min to get to A which is a total of 80min. The bus took 80 min to get from T to A. To get from A to T at the same speed (30mi/hr) it took the bus 80min. 80min = 80 min. This means going from A to T or vis versa at 30 mi/hr it will take the bus 80min.

2.A lady did not have her driver's license with her when she failed to stop at a stop sign and then went three blocks down a one-way street the wrong way. A policeman saw her, but he did not stop her. Explain.

' 'The lady was walking. It never says she was driving.

3.One of three boxes contains apples, another box contains oranges, and another box contains a mixture of apples and oranges. The boxes are labeled APPLES, ORANGES and APPLES AND ORANGES, but each label is incorrect. Can you select one fruit from only one box and determine the correct labels? Explain.

' 'if you selecet from the box APPLES AND ORANGES then you will be able to see the labels if they are correct or not.

4.I am the brother of the blind fiddler, but brothers I have none. How can this be?

' 'Since it says that he is the brother of the blind fiddler it does not mean that the fiddle is male, since he has no brothers than the fiddler must be a female.

5.Two quarters rest next to each other on a table. One coin is held fixed while the second coin is rolled around the edge of the first coin with no slipping. When the moving coin returns to its original position, how many times has it revolved?

' 'This is because the moving quarters revolves two full revolutions

6-10

Caitlin Lastiwka- Farquharson

6. Three kinds of apples are all mixed up in a basket. How many apples must you draw without (without looking) from the basket to be sure of getting at least two of a kind?

' ' To be sure you are getting at least two of a kind, you must select all of the other types of apples, plus two more. Meaning that only once you have selected all of the other apples can you be sure that you will select two of the kind you desire. It can be written like this: x,a x2, b and x3, c, with x representing the quantity of apples. This can be calculated by x2 + x3 +2. X2 representing one of the types of apples, x3 representing the other type and 2 representing 2 of the kind of apples you are trying to select. This is the only way to be sure you are getting at least two of a kind. ' '

7. Suppose you have 40 blue socks and 40 brown socks in a drawer. How many socks must you take from the drawer (without looking) to be sure of getting (i) a pair of the same colour, and (ii) a pair with different colors.

' 'You must take three socks from the drawer to ensure you have a pair that match. This is because if you only select two, one could be brown and one could be blue. Selecting three, ensures that at least two of them will be the same colour. As for part two, you would need to select 41 socks to ensure you had a pair of different coloured socks because if you select 40 or less you could get all the same colour, but selecting 41 ensures you will have at least one pair of mixed colour. ' '

8. Rueben says "Two days ago I was 20 years old. Later next year I will be 23 years old." Explain how this is possible.

' 'It is possible if your birthday is on the 31st of December and today is the 1st of January. This is because on the 30th of December (two days ago) you we’re 20 years old and now you are 21, later this year you will turn 22 on the 31st of December, and therefore 23 the next year.' '

9. A rope ladder hanging over the side of a boat has rungs one foot apart. Ten rungs are showing. If the tide rises five feet, how many rungs will be showing?

' ' 5 rungs will be showing, because if there are 10 showing now, and they are each a foot apart, then for 5 more rungs to be showing there would need to be an increase in the level of water by 5 feet. ' '

10.Suppose one-half of all people are chocolate eaters and one-half of all people are women. (i) Does it follow that one-fourth of all people are women chocolate eaters? (ii) Does it follow that one-half of all men are chocolate eaters? Explain.

' ' No, it does not follow that one-fourth of all people are women chocolate eaters and it does not follow that half of all men are chocolate eaters because are completely independent scenarios. Meaning that the the amount of women there are does not influence the amount of men that will eat chocolate. For example, If 50% of people are women and 50% of the entire population including men and women eat chocolate (arrived at by using the same logic that if 1/4 of women eat chocolate and 1/4 of men eat chocolate), that entire 50% could be comprised of women, meaning that no men eat chocolate disproving the statement.

11-14

Sifat Hasan

11. A woman, her older brother, her son, and her daughter are chess players. The worst player’s twin, who is one of the four players, and the best player are of opposite sex. The worst player and the best player have the same age. If this is possible, who is the worst player?

The four players (according to age, from oldest to youngest) are: woman's older brother, woman, and the son and the daughter (of the same age). Assuming that the children are of the same age (i.e. twins), the worst player is one of them, since they are the only ones who can have a twin. Assuming that the worst player is the daughter, her brother the son, is of the opposite sex as the woman, therefore the woman is the worst player. However, since the worst and the best player are of the same age, this is not possible, because the twins are of the opposite sex and they are of different genders.

12 A Manhattan fellow had a girlfriend in the Bronx and a girlfriend in Brooklyn. He decided which girlfriend to visit by arriving randomly at the train station and taking the first of the Bronx or Brooklyn trains that arrived. The trains to Brooklyn and the Bronx each arrived regularly every 10 minutes. Not long after he began his scheme the man's Bronx girlfriend left him because he rarely visited. Give a (logical) explanation

Assuming that the Bronx and the Brooklyn train arrive one after the other every 10 minutes, the only logical explanation would be that the man in Manhattan coincidentally went to the station 10 minutes or less before a train to Brooklyn arrived, most of the time.

13 If a clock takes 5 seconds to strike 5:00 (with 5 equally spaced chimes), how long does it take to strike 10:00 (with 10 equally spaced chimes)?

If it takes 5 seconds to strike 5, there will be 4 little halts in the middle. Therefore it takes 5 chimes 4 (5/4) = 1.25 second halts to finish. For 10 chimes, there are 9 halts so, it takes 9x 1.25 = 11.25 seconds for 10 halts.

14 One day in the maternity ward, the name tags for four girl babies became mixed up. (i) In how many different ways could two of the babies be tagged correctly and two of the babies be tagged incorrectly? (ii) In how many different ways could three of the babies be tagged correctly and one baby be tagged incorrectly?

(i)and (ii) If we take the babies names as A,B,C and D. There are 6 different combinations of the mix up, that two babies' names can be correct and 2 can be wrong. Assuming the name tags for the babies A,B,C and D are in respective order, they are ABDC, ADCB, ACBD, DBCA, CBAD and BACD. All other combinations for example BCAD will have one correct and 3 incorrect, or all four of them correct, because if 3 are correct, the fourth one has to be correct.

15-16

Roland Will

15. Alex says to you, “I'll bet you any amount of money that if I shuffle this deck of cards, there will always be as many red cards in the first half of the deck as there are black cards in the second half of the deck.” Should you accept his bet?

Answer: No, you shouldn't assuming the deck has equal amounts of red and black cards as in a standard 52 card deck.
Solution: In a standard 52 card deck, half of the cards (26) are black and half are red. If you take 26 cards at random from the deck, x of them will be black and y of them will be red, and x+y=26. As there are 26 of each color in the deck, then x+?=26 for the black cards in the deck and ?+y=26 for the red cards in the deck. As x+y=26 in the first randomly selected 26 cards, then the value of black cards in the other half of the deck must equal y, and the value of red cards in the other half of the deck must equal x meaning that "there will always be as many red cards in the first half of the deck as there are black cards in the second half of the deck."

16. Suppose that each daughter in your family has the same number of brothers as she has sisters, and each son in your family has twice as many sisters as he has brothers. How many sons and daughters are in the family?

Answer:3 total, 2 sister and 1 brother
Solution: Since the daughters in the family each have as many brothers as sisters the amount of sisters, with x standing for the amount of brothers, is x+1. As each brother has twice as many sisters as brothers, the amount of sisters must equal 2(x-1) or 2x-2. To find the number of brother: x+1=2x+1, 1=x-2, 3=x, which means that their are 3 brothers and 4 sisters (x+1= the number of sisters and x=3). This makes sense because a sister would have an equal amount of brothers to sisters, 3 sisters and 3 brothers, if there were 4 sisters and 3 brothers total, and each brother would have 4 sisters and 3 brothers, which is twice the amount of brothers to sisters.

17~21

Audrey Chen

17.The zero point on a bathroom scale is set incorrectly, but otherwise the scale is accurate. It shows 60 kg when Dan stands on the scale, 50 kg when Sarah stands on the scale, but 105 kg when Dan and Sarah both stand on the scale. Does the scale read too high or too low? Explain.

''The scale read too low, since Dan is shown as 60kg and Sarah is 50kg, suppose 60+50=110, 105-110=-5, so that means the scale is smaller than 0 in the beginning''

18. Alice takes one-third of the pennies from a large jar. Then Bret takes one-third of the remaining pennies from the jar. Finally, Carla takes one-third of the remaining pennies from the jar, leaving 40 pennies in the jar. How many pennies were in the jar at the start?

''If the total pennies is "x", Alice take 1/3x, so it has 2/3x left after Alice took it, than Bret take 1/3 out, after Alice took it, which is 2/3x*1/3= 2/9x, so in the beginning they have x, after Alice took it, it has 2/3x left, and Bret took 2/9x, so after Bret took it, it becomes 2/3x-2/9x= 4/9x-2/9x=2/9x left in the jar. Than Carla take 1/3 of the rest, so she took 1/3 of rest which is 2/9x*1/3=3/27x, so Alice took 1/3x, Bret tool 2/9x, Carla took 3/27x, three of them totaly took 1/3x+2/9x+3/27x=18/27x, so there still has x-18/27x= 9/27x= 1/3 left, 1/3x=40pennies, so x=120 pennies, so it was having 120 pennies in the jar.

19. One morning each member of Angela's family drank an eight-ounce cup of coffee and milk, with the (nonzero) amounts of coffee and milk varying from cup to cup. Angela drank a quarter of the total amount of milk and a sixth of the total amount of coffee. What is the least number of people in the family?

''If we let total milk is x, total coffee is y. Than 1/4x+1/6y=8, and because every cup is 8ounce, x+y is multiple by 8. So make it easier, we use 1/4x+1/6y=8 * 12 to both sides. than we will got 3x+2y=96, now we have 3x+2y=96 and x+y is multiple of 8, and the number that multiple by 8 is 8, 16, 24, 32... so 2x+2y= 16, 32, 48, 64, 80, 96, since 3x+2y=96, it can't be more than 96. It will only have 6 possible number, so if you take 3x+2y=96 substracting 2x+2y=16, 32, 48, 64, 80, 96 you can get 6 possible x, which are 80, 64, 48, 32, 16, and 0. Than put the number into 3x+2y=96, if you put 80 in, will get 20, which is bigger than 8, and also 64, 48. If we use 32, it will equal to 8, but that means we have 0 coffee, but coffee can't be 0, so there's only 16 and 0 left. Since Angela had 1/4 of total amount of milk, milk can't be 0. So we got 16ounce than 16*(1/4)=4, so that means she had 8-4=4 's coffee. So 4=1/6 coffee, than the total amount of coffee would be 4*6=24. than x=16 and y=24, 16+24=40 40/8ounce=5, so at least have 5 cups of drinks, so that means at least they have 5 members in Angela's family.''

20.Of two clocks next to each other, one runs 5 min per hour fast and the other runs 5 min per hour slow. At midnight the clocks show the same time. At what time are they are one hour apart?

''Since one clock runs 5 min faster per hour, the other is 5 min slower, after clock runs an hour, two clocks will have 10 min different from each other. 60 min an hour. 60/10=6, so after 6 hours two clocks will having one hour apart, and that would be 6AM.''

21.Sven placed exactly in the middle among all runners in a race. Dan was slower than Sven, in 10th place, and Lars was in 16th place. How many runners were in the race?

''There were 17 runners. Since lars was in 16th place, the runners at least have to be 16, than if Sven is placed exactly in the middle, it means it would have even number of runners. Because Dan is slower and he was at 10 place that tells us Seven has to be before 10th, and if there has 19 runners, Sven and Dan would be at the same place, so it should be 17 runners, than Sven would be at exactly in the middle which at 9th place.''

22-25

Roland Will

22. During a vacation, it rained on 13 days, but when it rained in the morning, the afternoon was sunny, and every rainy afternoon was preceded by a sunny morning. There were 11 sunny mornings and 12 sunny afternoons. How long was the vacation?

Answer: 18 days of vacation.

Solution: 13 of the days of vacation were half sunny and half rainy. As there were 23 sunny mornings and afternoons (11 sunny mornings+12 sunny afternoons = 23 sunny mornings and afternoons), 13 of those sunny afternoons or mornings were on half rainy days. This means there are 10 sunny half-days left over, which equal 5 sunny full days. The 5 sunny full days plus the 13 half sunny/rainy days equal 18 total days of vacation.

23. Suppose you overhear the following conversation: Paul: How old are your three children? Paula: The product of their ages is 36 and the sum of their ages is the same as today's date. Paul: That is not enough information. Paula: The oldest child also has red hair. If you were Paul could you determine the ages of Paula's children? Explain.

Answer: If I were Paul this might be possible, but since we don’t know the date that Paula said this, it is not possible for us to find out.

Solution: There are many different combinations of three numbers that can be multiplied and will produce 36. As we do not know the date that Paula said this, the only thing we can be sure of is that the sum of the ages is less than 31 because no month has more than 31 days. Unfortunately, only one set of ages (ages 1 year old, 1 year old and 36 years old) has a sum greater than 31, which leaves many possible combinations open as possible. For today’s date, the 13th, ages of 2, 2, and 9 would produce 36 and have a sum of 13, but, again, it is uncertain. If it were the first of the month, there would be no possible combinations that would produce 36 and sum 1.

24. Two candles of equal length were lit at the same time. One candle took 6 hr to burn out and the other candle took 3 hr to burn out. After how much time was one candle exactly twice as long as the other candle?

Answer: 2 hours.

Solution: The faster burning candle took half the time to burn as the slower burning candle (3 hours/ 6 hours = 1/2), meaning it burned twice as fast. This means that after 2/3 of the total burning time for the faster burning candle it will be 1/3 of its original height and at the slower burning candle will be at 2/3 of its original height and 1/3 is half of 2/3. Since the faster burning candle took 3 hours to burn, 2/3 of its total burning time is 2 hours.

25. Two candles of length L and L + 1 were lit at 6:00 and 4:30, respectively. At 8:30 they had the same length. The longer candle died at 10:30 and the shorter candle died at 10:00. Find L.

Answer: L=2.

Solution: The shorter candle lasted for 4 hours and the longer candle lasted for 6 hours. As 6 hours – 4 hours = 2 hours and 2 hours / 4 hours = 1/2, the longer candle lasted 50% longer and was, therefore, 50% longer in length. This means that the +1 in L+1 on the longer candle was 1/2 of L. 1/2L=1, so L=2*1, L=2.

Course:MATH110/Archive/2010-2011/003/Groups/Group 18

2010-11-12T05:27:57Z

RolandWill: /* 21.Sven placed exactly in the middle among all runners in a race. Dan was slower than Sven, in 10th place, and Lars was in 16th place. How many runners were in the race? */

{{Infobox MATH110 Groups
| group number = 18
| member 1 = [[User:ChouJuChen|Audrey Chen]]
| member 2 = [[User:SifatHasan|Sifat Hasan]]
| member 3 = [[User:CaitlinLastiwkaFarquharson|Caitlin Lastiwka-Farquharson]]
| member 4 = [[User:VictoriaWall|Victoria Wall]]
| member 5 = [[User:RolandWill|Roland Will]]
| member 6 =
}}

==Sub-Pages==

Basic Skills Project [http://wiki.ubc.ca/Course:MATH110/003/Groups/Group_18/Basic_Skills_Project]

==Homework due October 20th, 2010==

I created a page for our homework due tomorrow: [http://wiki.ubc.ca/Course:MATH110/003/Groups/Group_18/Homework_October_20th,_2010 http://wiki.ubc.ca/Course:MATH110/003/Groups/Group 18/Homework October 20th, 2010]

-Roland

I've moved the page, it was missing the ''Course:'' part which means it was created directly inside the wiki and not as a subpage of your group page, which is something the wiki admins don't like that much. By the way, you're allowed to use spaces in the name of your pages.

-- [[User:DavidKohler|DavidKohler]] 06:28, 20 October 2010 (UTC)

1-5

Victoria Wall

1.A bus traveled from the terminal to the airport at an average speed of 30 mi/hr and the trip took an hour and 20 min. The bus then traveled from the airport back to the terminal and again averaged 30 mi/hr. However, the return trip required 80 min. Explain.

' 'Lets call the terminal T and the airport A. If the bus travelled from T to A at 30mi/hr and it took them one hour and 20 mins to get from T to A at this speed, and there are 60 minutes in one hour, it took the bus 60min + 20min to get to A which is a total of 80min. The bus took 80 min to get from T to A. To get from A to T at the same speed (30mi/hr) it took the bus 80min. 80min = 80 min. This means going from A to T or vis versa at 30 mi/hr it will take the bus 80min.

2.A lady did not have her driver's license with her when she failed to stop at a stop sign and then went three blocks down a one-way street the wrong way. A policeman saw her, but he did not stop her. Explain.

' 'The lady was walking. It never says she was driving.

3.One of three boxes contains apples, another box contains oranges, and another box contains a mixture of apples and oranges. The boxes are labeled APPLES, ORANGES and APPLES AND ORANGES, but each label is incorrect. Can you select one fruit from only one box and determine the correct labels? Explain.

' 'if you selecet from the box APPLES AND ORANGES then you will be able to see the labels if they are correct or not.

4.I am the brother of the blind fiddler, but brothers I have none. How can this be?

' 'Since it says that he is the brother of the blind fiddler it does not mean that the fiddle is male, since he has no brothers than the fiddler must be a female.

5.Two quarters rest next to each other on a table. One coin is held fixed while the second coin is rolled around the edge of the first coin with no slipping. When the moving coin returns to its original position, how many times has it revolved?

' 'This is because the moving quarters revolves two full revolutions

6-10

Caitlin Lastiwka- Farquharson

6. Three kinds of apples are all mixed up in a basket. How many apples must you draw without (without looking) from the basket to be sure of getting at least two of a kind?

' ' To be sure you are getting at least two of a kind, you must select all of the other types of apples, plus two more. Meaning that only once you have selected all of the other apples can you be sure that you will select two of the kind you desire. It can be written like this: x,a x2, b and x3, c, with x representing the quantity of apples. This can be calculated by x2 + x3 +2. X2 representing one of the types of apples, x3 representing the other type and 2 representing 2 of the kind of apples you are trying to select. This is the only way to be sure you are getting at least two of a kind. ' '

7. Suppose you have 40 blue socks and 40 brown socks in a drawer. How many socks must you take from the drawer (without looking) to be sure of getting (i) a pair of the same colour, and (ii) a pair with different colors.

' 'You must take three socks from the drawer to ensure you have a pair that match. This is because if you only select two, one could be brown and one could be blue. Selecting three, ensures that at least two of them will be the same colour. As for part two, you would need to select 41 socks to ensure you had a pair of different coloured socks because if you select 40 or less you could get all the same colour, but selecting 41 ensures you will have at least one pair of mixed colour. ' '

8. Rueben says "Two days ago I was 20 years old. Later next year I will be 23 years old." Explain how this is possible.

' 'It is possible if your birthday is on the 31st of December and today is the 1st of January. This is because on the 30th of December (two days ago) you we’re 20 years old and now you are 21, later this year you will turn 22 on the 31st of December, and therefore 23 the next year.' '

9. A rope ladder hanging over the side of a boat has rungs one foot apart. Ten rungs are showing. If the tide rises five feet, how many rungs will be showing?

' ' 5 rungs will be showing, because if there are 10 showing now, and they are each a foot apart, then for 5 more rungs to be showing there would need to be an increase in the level of water by 5 feet. ' '

10.Suppose one-half of all people are chocolate eaters and one-half of all people are women. (i) Does it follow that one-fourth of all people are women chocolate eaters? (ii) Does it follow that one-half of all men are chocolate eaters? Explain.

' ' No, it does not follow that one-fourth of all people are women chocolate eaters and it does not follow that half of all men are chocolate eaters because are completely independent scenarios. Meaning that the the amount of women there are does not influence the amount of men that will eat chocolate. For example, If 50% of people are women and 50% of the entire population including men and women eat chocolate (arrived at by using the same logic that if 1/4 of women eat chocolate and 1/4 of men eat chocolate), that entire 50% could be comprised of women, meaning that no men eat chocolate disproving the statement.

11-14

Sifat Hasan

11. A woman, her older brother, her son, and her daughter are chess players. The worst player’s twin, who is one of the four players, and the best player are of opposite sex. The worst player and the best player have the same age. If this is possible, who is the worst player?

The four players (according to age, from oldest to youngest) are: woman's older brother, woman, and the son and the daughter (of the same age). Assuming that the children are of the same age (i.e. twins), the worst player is one of them, since they are the only ones who can have a twin. Assuming that the worst player is the daughter, her brother the son, is of the opposite sex as the woman, therefore the woman is the worst player. However, since the worst and the best player are of the same age, this is not possible, because the twins are of the opposite sex and they are of different genders.

12 A Manhattan fellow had a girlfriend in the Bronx and a girlfriend in Brooklyn. He decided which girlfriend to visit by arriving randomly at the train station and taking the first of the Bronx or Brooklyn trains that arrived. The trains to Brooklyn and the Bronx each arrived regularly every 10 minutes. Not long after he began his scheme the man's Bronx girlfriend left him because he rarely visited. Give a (logical) explanation

Assuming that the Bronx and the Brooklyn train arrive one after the other every 10 minutes, the only logical explanation would be that the man in Manhattan coincidentally went to the station 10 minutes or less before a train to Brooklyn arrived, most of the time.

13 If a clock takes 5 seconds to strike 5:00 (with 5 equally spaced chimes), how long does it take to strike 10:00 (with 10 equally spaced chimes)?

If it takes 5 seconds to strike 5, there will be 4 little halts in the middle. Therefore it takes 5 chimes 4 (5/4) = 1.25 second halts to finish. For 10 chimes, there are 9 halts so, it takes 9x 1.25 = 11.25 seconds for 10 halts.

14 One day in the maternity ward, the name tags for four girl babies became mixed up. (i) In how many different ways could two of the babies be tagged correctly and two of the babies be tagged incorrectly? (ii) In how many different ways could three of the babies be tagged correctly and one baby be tagged incorrectly?

(i)and (ii) If we take the babies names as A,B,C and D. There are 6 different combinations of the mix up, that two babies' names can be correct and 2 can be wrong. Assuming the name tags for the babies A,B,C and D are in respective order, they are ABDC, ADCB, ACBD, DBCA, CBAD and BACD. All other combinations for example BCAD will have one correct and 3 incorrect, or all four of them correct, because if 3 are correct, the fourth one has to be correct.

15-16

Roland Will

15. Alex says to you, “I'll bet you any amount of money that if I shuffle this deck of cards, there will always be as many red cards in the first half of the deck as there are black cards in the second half of the deck.” Should you accept his bet?

Answer: No, you shouldn't assuming the deck has equal amounts of red and black cards as in a standard 52 card deck.
Solution: In a standard 52 card deck, half of the cards (26) are black and half are red. If you take 26 cards at random from the deck, x of them will be black and y of them will be red, and x+y=26. As there are 26 of each color in the deck, then x+?=26 for the black cards in the deck and ?+y=26 for the red cards in the deck. As x+y=26 in the first randomly selected 26 cards, then the value of black cards in the other half of the deck must equal y, and the value of red cards in the other half of the deck must equal x meaning that "there will always be as many red cards in the first half of the deck as there are black cards in the second half of the deck."

16. Suppose that each daughter in your family has the same number of brothers as she has sisters, and each son in your family has twice as many sisters as he has brothers. How many sons and daughters are in the family?

Answer:3 total, 2 sister and 1 brother
Solution: Since the daughters in the family each have as many brothers as sisters the amount of sisters, with x standing for the amount of brothers, is x+1. As each brother has twice as many sisters as brothers, the amount of sisters must equal 2(x-1) or 2x-2. To find the number of brother: x+1=2x+1, 1=x-2, 3=x, which means that their are 3 brothers and 4 sisters (x+1= the number of sisters and x=3). This makes sense because a sister would have an equal amount of brothers to sisters, 3 sisters and 3 brothers, if there were 4 sisters and 3 brothers total, and each brother would have 4 sisters and 3 brothers, which is twice the amount of brothers to sisters.

17~21

Audrey Chen

17.The zero point on a bathroom scale is set incorrectly, but otherwise the scale is accurate. It shows 60 kg when Dan stands on the scale, 50 kg when Sarah stands on the scale, but 105 kg when Dan and Sarah both stand on the scale. Does the scale read too high or too low? Explain.

''The scale read too low, since Dan is shown as 60kg and Sarah is 50kg, suppose 60+50=110, 105-110=-5, so that means the scale is smaller than 0 in the beginning''

18. Alice takes one-third of the pennies from a large jar. Then Bret takes one-third of the remaining pennies from the jar. Finally, Carla takes one-third of the remaining pennies from the jar, leaving 40 pennies in the jar. How many pennies were in the jar at the start?

''If the total pennies is "x", Alice take 1/3x, so it has 2/3x left after Alice took it, than Bret take 1/3 out, after Alice took it, which is 2/3x*1/3= 2/9x, so in the beginning they have x, after Alice took it, it has 2/3x left, and Bret took 2/9x, so after Bret took it, it becomes 2/3x-2/9x= 4/9x-2/9x=2/9x left in the jar. Than Carla take 1/3 of the rest, so she took 1/3 of rest which is 2/9x*1/3=3/27x, so Alice took 1/3x, Bret tool 2/9x, Carla took 3/27x, three of them totaly took 1/3x+2/9x+3/27x=18/27x, so there still has x-18/27x= 9/27x= 1/3 left, 1/3x=40pennies, so x=120 pennies, so it was having 120 pennies in the jar.

19. One morning each member of Angela's family drank an eight-ounce cup of coffee and milk, with the (nonzero) amounts of coffee and milk varying from cup to cup. Angela drank a quarter of the total amount of milk and a sixth of the total amount of coffee. What is the least number of people in the family?

''If we let total milk is x, total coffee is y. Than 1/4x+1/6y=8, and because every cup is 8ounce, x+y is multiple by 8. So make it easier, we use 1/4x+1/6y=8 * 12 to both sides. than we will got 3x+2y=96, now we have 3x+2y=96 and x+y is multiple of 8, and the number that multiple by 8 is 8, 16, 24, 32... so 2x+2y= 16, 32, 48, 64, 80, 96, since 3x+2y=96, it can't be more than 96. It will only have 6 possible number, so if you take 3x+2y=96 substracting 2x+2y=16, 32, 48, 64, 80, 96 you can get 6 possible x, which are 80, 64, 48, 32, 16, and 0. Than put the number into 3x+2y=96, if you put 80 in, will get 20, which is bigger than 8, and also 64, 48. If we use 32, it will equal to 8, but that means we have 0 coffee, but coffee can't be 0, so there's only 16 and 0 left. Since Angela had 1/4 of total amount of milk, milk can't be 0. So we got 16ounce than 16*(1/4)=4, so that means she had 8-4=4 's coffee. So 4=1/6 coffee, than the total amount of coffee would be 4*6=24. than x=16 and y=24, 16+24=40 40/8ounce=5, so at least have 5 cups of drinks, so that means at least they have 5 members in Angela's family.''

20.Of two clocks next to each other, one runs 5 min per hour fast and the other runs 5 min per hour slow. At midnight the clocks show the same time. At what time are they are one hour apart?

''Since one clock runs 5 min faster per hour, the other is 5 min slower, after clock runs an hour, two clocks will have 10 min different from each other. 60 min an hour. 60/10=6, so after 6 hours two clocks will having one hour apart, and that would be 6AM.''

21.Sven placed exactly in the middle among all runners in a race. Dan was slower than Sven, in 10th place, and Lars was in 16th place. How many runners were in the race?

''There were 17 runners. Since lars was in 16th place, the runners at least have to be 16, than if Sven is placed exactly in the middle, it means it would have even number of runners. Because Dan is slower and he was at 10 place that tells us Seven has to be before 10th, and if there has 19 runners, Sven and Dan would be at the same place, so it should be 17 runners, than Sven would be at exactly in the middle which at 9th place.''

==22-25==

Roland Will

22. During a vacation, it rained on 13 days, but when it rained in the morning, the afternoon was sunny, and every rainy afternoon was preceded by a sunny morning. There were 11 sunny mornings and 12 sunny afternoons. How long was the vacation?

Answer: 18 days of vacation.

Solution: 13 of the days of vacation were half sunny and half rainy. As there were 23 sunny mornings and afternoons (11 sunny mornings+12 sunny afternoons = 23 sunny mornings and afternoons), 13 of those sunny afternoons or mornings were on half rainy days. This means there are 10 sunny half-days left over, which equal 5 sunny full days. The 5 sunny full days plus the 13 half sunny/rainy days equal 18 total days of vacation.

23. Suppose you overhear the following conversation: Paul: How old are your three children? Paula: The product of their ages is 36 and the sum of their ages is the same as today's date. Paul: That is not enough information. Paula: The oldest child also has red hair. If you were Paul could you determine the ages of Paula's children? Explain.

Answer: If I were Paul this might be possible, but since we don’t know the date that Paula said this, it is not possible for us to find out.

Solution: There are many different combinations of three numbers that can be multiplied and will produce 36. As we do not know the date that Paula said this, the only thing we can be sure of is that the sum of the ages is less than 31 because no month has more than 31 days. Unfortunately, only one set of ages (ages 1 year old, 1 year old and 36 years old) has a sum greater than 31, which leaves many possible combinations open as possible. For today’s date, the 13th, ages of 2, 2, and 9 would produce 36 and have a sum of 13, but, again, it is uncertain. If it were the first of the month, there would be no possible combinations that would produce 36 and sum 1.

24. Two candles of equal length were lit at the same time. One candle took 6 hr to burn out and the other candle took 3 hr to burn out. After how much time was one candle exactly twice as long as the other candle?

Answer: 2 hours.

Solution: The faster burning candle took half the time to burn as the slower burning candle (3 hours/ 6 hours = 1/2), meaning it burned twice as fast. This means that after 2/3 of the total burning time for the faster burning candle it will be 1/3 of its original height and at the slower burning candle will be at 2/3 of its original height and 1/3 is half of 2/3. Since the faster burning candle took 3 hours to burn, 2/3 of its total burning time is 2 hours.

25. Two candles of length L and L + 1 were lit at 6:00 and 4:30, respectively. At 8:30 they had the same length. The longer candle died at 10:30 and the shorter candle died at 10:00. Find L.

Answer: L=2.

Solution: The shorter candle lasted for 4 hours and the longer candle lasted for 6 hours. As 6 hours – 4 hours = 2 hours and 2 hours / 4 hours = 1/2, the longer candle lasted 50% longer and was, therefore, 50% longer in length. This means that the +1 in L+1 on the longer candle was 1/2 of L. 1/2L=1, so L=2*1, L=2.

Course:MATH110/Archive/2010-2011/003/Groups/Group 18

2010-11-12T05:27:48Z

RolandWill: /* 20.Of two clocks next to each other, one runs 5 min per hour fast and the other runs 5 min per hour slow. At midnight the clocks show the same time. At what time are they are one hour apart? */

{{Infobox MATH110 Groups
| group number = 18
| member 1 = [[User:ChouJuChen|Audrey Chen]]
| member 2 = [[User:SifatHasan|Sifat Hasan]]
| member 3 = [[User:CaitlinLastiwkaFarquharson|Caitlin Lastiwka-Farquharson]]
| member 4 = [[User:VictoriaWall|Victoria Wall]]
| member 5 = [[User:RolandWill|Roland Will]]
| member 6 =
}}

==Sub-Pages==

Basic Skills Project [http://wiki.ubc.ca/Course:MATH110/003/Groups/Group_18/Basic_Skills_Project]

==Homework due October 20th, 2010==

I created a page for our homework due tomorrow: [http://wiki.ubc.ca/Course:MATH110/003/Groups/Group_18/Homework_October_20th,_2010 http://wiki.ubc.ca/Course:MATH110/003/Groups/Group 18/Homework October 20th, 2010]

-Roland

I've moved the page, it was missing the ''Course:'' part which means it was created directly inside the wiki and not as a subpage of your group page, which is something the wiki admins don't like that much. By the way, you're allowed to use spaces in the name of your pages.

-- [[User:DavidKohler|DavidKohler]] 06:28, 20 October 2010 (UTC)

1-5

Victoria Wall

1.A bus traveled from the terminal to the airport at an average speed of 30 mi/hr and the trip took an hour and 20 min. The bus then traveled from the airport back to the terminal and again averaged 30 mi/hr. However, the return trip required 80 min. Explain.

' 'Lets call the terminal T and the airport A. If the bus travelled from T to A at 30mi/hr and it took them one hour and 20 mins to get from T to A at this speed, and there are 60 minutes in one hour, it took the bus 60min + 20min to get to A which is a total of 80min. The bus took 80 min to get from T to A. To get from A to T at the same speed (30mi/hr) it took the bus 80min. 80min = 80 min. This means going from A to T or vis versa at 30 mi/hr it will take the bus 80min.

2.A lady did not have her driver's license with her when she failed to stop at a stop sign and then went three blocks down a one-way street the wrong way. A policeman saw her, but he did not stop her. Explain.

' 'The lady was walking. It never says she was driving.

3.One of three boxes contains apples, another box contains oranges, and another box contains a mixture of apples and oranges. The boxes are labeled APPLES, ORANGES and APPLES AND ORANGES, but each label is incorrect. Can you select one fruit from only one box and determine the correct labels? Explain.

' 'if you selecet from the box APPLES AND ORANGES then you will be able to see the labels if they are correct or not.

4.I am the brother of the blind fiddler, but brothers I have none. How can this be?

' 'Since it says that he is the brother of the blind fiddler it does not mean that the fiddle is male, since he has no brothers than the fiddler must be a female.

5.Two quarters rest next to each other on a table. One coin is held fixed while the second coin is rolled around the edge of the first coin with no slipping. When the moving coin returns to its original position, how many times has it revolved?

' 'This is because the moving quarters revolves two full revolutions

6-10

Caitlin Lastiwka- Farquharson

6. Three kinds of apples are all mixed up in a basket. How many apples must you draw without (without looking) from the basket to be sure of getting at least two of a kind?

' ' To be sure you are getting at least two of a kind, you must select all of the other types of apples, plus two more. Meaning that only once you have selected all of the other apples can you be sure that you will select two of the kind you desire. It can be written like this: x,a x2, b and x3, c, with x representing the quantity of apples. This can be calculated by x2 + x3 +2. X2 representing one of the types of apples, x3 representing the other type and 2 representing 2 of the kind of apples you are trying to select. This is the only way to be sure you are getting at least two of a kind. ' '

7. Suppose you have 40 blue socks and 40 brown socks in a drawer. How many socks must you take from the drawer (without looking) to be sure of getting (i) a pair of the same colour, and (ii) a pair with different colors.

' 'You must take three socks from the drawer to ensure you have a pair that match. This is because if you only select two, one could be brown and one could be blue. Selecting three, ensures that at least two of them will be the same colour. As for part two, you would need to select 41 socks to ensure you had a pair of different coloured socks because if you select 40 or less you could get all the same colour, but selecting 41 ensures you will have at least one pair of mixed colour. ' '

8. Rueben says "Two days ago I was 20 years old. Later next year I will be 23 years old." Explain how this is possible.

' 'It is possible if your birthday is on the 31st of December and today is the 1st of January. This is because on the 30th of December (two days ago) you we’re 20 years old and now you are 21, later this year you will turn 22 on the 31st of December, and therefore 23 the next year.' '

9. A rope ladder hanging over the side of a boat has rungs one foot apart. Ten rungs are showing. If the tide rises five feet, how many rungs will be showing?

' ' 5 rungs will be showing, because if there are 10 showing now, and they are each a foot apart, then for 5 more rungs to be showing there would need to be an increase in the level of water by 5 feet. ' '

10.Suppose one-half of all people are chocolate eaters and one-half of all people are women. (i) Does it follow that one-fourth of all people are women chocolate eaters? (ii) Does it follow that one-half of all men are chocolate eaters? Explain.

' ' No, it does not follow that one-fourth of all people are women chocolate eaters and it does not follow that half of all men are chocolate eaters because are completely independent scenarios. Meaning that the the amount of women there are does not influence the amount of men that will eat chocolate. For example, If 50% of people are women and 50% of the entire population including men and women eat chocolate (arrived at by using the same logic that if 1/4 of women eat chocolate and 1/4 of men eat chocolate), that entire 50% could be comprised of women, meaning that no men eat chocolate disproving the statement.

11-14

Sifat Hasan

11. A woman, her older brother, her son, and her daughter are chess players. The worst player’s twin, who is one of the four players, and the best player are of opposite sex. The worst player and the best player have the same age. If this is possible, who is the worst player?

The four players (according to age, from oldest to youngest) are: woman's older brother, woman, and the son and the daughter (of the same age). Assuming that the children are of the same age (i.e. twins), the worst player is one of them, since they are the only ones who can have a twin. Assuming that the worst player is the daughter, her brother the son, is of the opposite sex as the woman, therefore the woman is the worst player. However, since the worst and the best player are of the same age, this is not possible, because the twins are of the opposite sex and they are of different genders.

12 A Manhattan fellow had a girlfriend in the Bronx and a girlfriend in Brooklyn. He decided which girlfriend to visit by arriving randomly at the train station and taking the first of the Bronx or Brooklyn trains that arrived. The trains to Brooklyn and the Bronx each arrived regularly every 10 minutes. Not long after he began his scheme the man's Bronx girlfriend left him because he rarely visited. Give a (logical) explanation

Assuming that the Bronx and the Brooklyn train arrive one after the other every 10 minutes, the only logical explanation would be that the man in Manhattan coincidentally went to the station 10 minutes or less before a train to Brooklyn arrived, most of the time.

13 If a clock takes 5 seconds to strike 5:00 (with 5 equally spaced chimes), how long does it take to strike 10:00 (with 10 equally spaced chimes)?

If it takes 5 seconds to strike 5, there will be 4 little halts in the middle. Therefore it takes 5 chimes 4 (5/4) = 1.25 second halts to finish. For 10 chimes, there are 9 halts so, it takes 9x 1.25 = 11.25 seconds for 10 halts.

14 One day in the maternity ward, the name tags for four girl babies became mixed up. (i) In how many different ways could two of the babies be tagged correctly and two of the babies be tagged incorrectly? (ii) In how many different ways could three of the babies be tagged correctly and one baby be tagged incorrectly?

(i)and (ii) If we take the babies names as A,B,C and D. There are 6 different combinations of the mix up, that two babies' names can be correct and 2 can be wrong. Assuming the name tags for the babies A,B,C and D are in respective order, they are ABDC, ADCB, ACBD, DBCA, CBAD and BACD. All other combinations for example BCAD will have one correct and 3 incorrect, or all four of them correct, because if 3 are correct, the fourth one has to be correct.

15-16

Roland Will

15. Alex says to you, “I'll bet you any amount of money that if I shuffle this deck of cards, there will always be as many red cards in the first half of the deck as there are black cards in the second half of the deck.” Should you accept his bet?

Answer: No, you shouldn't assuming the deck has equal amounts of red and black cards as in a standard 52 card deck.
Solution: In a standard 52 card deck, half of the cards (26) are black and half are red. If you take 26 cards at random from the deck, x of them will be black and y of them will be red, and x+y=26. As there are 26 of each color in the deck, then x+?=26 for the black cards in the deck and ?+y=26 for the red cards in the deck. As x+y=26 in the first randomly selected 26 cards, then the value of black cards in the other half of the deck must equal y, and the value of red cards in the other half of the deck must equal x meaning that "there will always be as many red cards in the first half of the deck as there are black cards in the second half of the deck."

16. Suppose that each daughter in your family has the same number of brothers as she has sisters, and each son in your family has twice as many sisters as he has brothers. How many sons and daughters are in the family?

Answer:3 total, 2 sister and 1 brother
Solution: Since the daughters in the family each have as many brothers as sisters the amount of sisters, with x standing for the amount of brothers, is x+1. As each brother has twice as many sisters as brothers, the amount of sisters must equal 2(x-1) or 2x-2. To find the number of brother: x+1=2x+1, 1=x-2, 3=x, which means that their are 3 brothers and 4 sisters (x+1= the number of sisters and x=3). This makes sense because a sister would have an equal amount of brothers to sisters, 3 sisters and 3 brothers, if there were 4 sisters and 3 brothers total, and each brother would have 4 sisters and 3 brothers, which is twice the amount of brothers to sisters.

17~21

Audrey Chen

17.The zero point on a bathroom scale is set incorrectly, but otherwise the scale is accurate. It shows 60 kg when Dan stands on the scale, 50 kg when Sarah stands on the scale, but 105 kg when Dan and Sarah both stand on the scale. Does the scale read too high or too low? Explain.

''The scale read too low, since Dan is shown as 60kg and Sarah is 50kg, suppose 60+50=110, 105-110=-5, so that means the scale is smaller than 0 in the beginning''

18. Alice takes one-third of the pennies from a large jar. Then Bret takes one-third of the remaining pennies from the jar. Finally, Carla takes one-third of the remaining pennies from the jar, leaving 40 pennies in the jar. How many pennies were in the jar at the start?

''If the total pennies is "x", Alice take 1/3x, so it has 2/3x left after Alice took it, than Bret take 1/3 out, after Alice took it, which is 2/3x*1/3= 2/9x, so in the beginning they have x, after Alice took it, it has 2/3x left, and Bret took 2/9x, so after Bret took it, it becomes 2/3x-2/9x= 4/9x-2/9x=2/9x left in the jar. Than Carla take 1/3 of the rest, so she took 1/3 of rest which is 2/9x*1/3=3/27x, so Alice took 1/3x, Bret tool 2/9x, Carla took 3/27x, three of them totaly took 1/3x+2/9x+3/27x=18/27x, so there still has x-18/27x= 9/27x= 1/3 left, 1/3x=40pennies, so x=120 pennies, so it was having 120 pennies in the jar.

19. One morning each member of Angela's family drank an eight-ounce cup of coffee and milk, with the (nonzero) amounts of coffee and milk varying from cup to cup. Angela drank a quarter of the total amount of milk and a sixth of the total amount of coffee. What is the least number of people in the family?

''If we let total milk is x, total coffee is y. Than 1/4x+1/6y=8, and because every cup is 8ounce, x+y is multiple by 8. So make it easier, we use 1/4x+1/6y=8 * 12 to both sides. than we will got 3x+2y=96, now we have 3x+2y=96 and x+y is multiple of 8, and the number that multiple by 8 is 8, 16, 24, 32... so 2x+2y= 16, 32, 48, 64, 80, 96, since 3x+2y=96, it can't be more than 96. It will only have 6 possible number, so if you take 3x+2y=96 substracting 2x+2y=16, 32, 48, 64, 80, 96 you can get 6 possible x, which are 80, 64, 48, 32, 16, and 0. Than put the number into 3x+2y=96, if you put 80 in, will get 20, which is bigger than 8, and also 64, 48. If we use 32, it will equal to 8, but that means we have 0 coffee, but coffee can't be 0, so there's only 16 and 0 left. Since Angela had 1/4 of total amount of milk, milk can't be 0. So we got 16ounce than 16*(1/4)=4, so that means she had 8-4=4 's coffee. So 4=1/6 coffee, than the total amount of coffee would be 4*6=24. than x=16 and y=24, 16+24=40 40/8ounce=5, so at least have 5 cups of drinks, so that means at least they have 5 members in Angela's family.''

20.Of two clocks next to each other, one runs 5 min per hour fast and the other runs 5 min per hour slow. At midnight the clocks show the same time. At what time are they are one hour apart?

''Since one clock runs 5 min faster per hour, the other is 5 min slower, after clock runs an hour, two clocks will have 10 min different from each other. 60 min an hour. 60/10=6, so after 6 hours two clocks will having one hour apart, and that would be 6AM.''

==21.Sven placed exactly in the middle among all runners in a race. Dan was slower than Sven, in 10th place, and Lars was in 16th place. How many runners were in the race? ==

''There were 17 runners. Since lars was in 16th place, the runners at least have to be 16, than if Sven is placed exactly in the middle, it means it would have even number of runners. Because Dan is slower and he was at 10 place that tells us Seven has to be before 10th, and if there has 19 runners, Sven and Dan would be at the same place, so it should be 17 runners, than Sven would be at exactly in the middle which at 9th place.''

==22-25==

Roland Will

22. During a vacation, it rained on 13 days, but when it rained in the morning, the afternoon was sunny, and every rainy afternoon was preceded by a sunny morning. There were 11 sunny mornings and 12 sunny afternoons. How long was the vacation?

Answer: 18 days of vacation.

Solution: 13 of the days of vacation were half sunny and half rainy. As there were 23 sunny mornings and afternoons (11 sunny mornings+12 sunny afternoons = 23 sunny mornings and afternoons), 13 of those sunny afternoons or mornings were on half rainy days. This means there are 10 sunny half-days left over, which equal 5 sunny full days. The 5 sunny full days plus the 13 half sunny/rainy days equal 18 total days of vacation.

23. Suppose you overhear the following conversation: Paul: How old are your three children? Paula: The product of their ages is 36 and the sum of their ages is the same as today's date. Paul: That is not enough information. Paula: The oldest child also has red hair. If you were Paul could you determine the ages of Paula's children? Explain.

Answer: If I were Paul this might be possible, but since we don’t know the date that Paula said this, it is not possible for us to find out.

Solution: There are many different combinations of three numbers that can be multiplied and will produce 36. As we do not know the date that Paula said this, the only thing we can be sure of is that the sum of the ages is less than 31 because no month has more than 31 days. Unfortunately, only one set of ages (ages 1 year old, 1 year old and 36 years old) has a sum greater than 31, which leaves many possible combinations open as possible. For today’s date, the 13th, ages of 2, 2, and 9 would produce 36 and have a sum of 13, but, again, it is uncertain. If it were the first of the month, there would be no possible combinations that would produce 36 and sum 1.

24. Two candles of equal length were lit at the same time. One candle took 6 hr to burn out and the other candle took 3 hr to burn out. After how much time was one candle exactly twice as long as the other candle?

Answer: 2 hours.

Solution: The faster burning candle took half the time to burn as the slower burning candle (3 hours/ 6 hours = 1/2), meaning it burned twice as fast. This means that after 2/3 of the total burning time for the faster burning candle it will be 1/3 of its original height and at the slower burning candle will be at 2/3 of its original height and 1/3 is half of 2/3. Since the faster burning candle took 3 hours to burn, 2/3 of its total burning time is 2 hours.

25. Two candles of length L and L + 1 were lit at 6:00 and 4:30, respectively. At 8:30 they had the same length. The longer candle died at 10:30 and the shorter candle died at 10:00. Find L.

Answer: L=2.

Solution: The shorter candle lasted for 4 hours and the longer candle lasted for 6 hours. As 6 hours – 4 hours = 2 hours and 2 hours / 4 hours = 1/2, the longer candle lasted 50% longer and was, therefore, 50% longer in length. This means that the +1 in L+1 on the longer candle was 1/2 of L. 1/2L=1, so L=2*1, L=2.

Course:MATH110/Archive/2010-2011/003/Groups/Group 18

2010-11-12T05:27:37Z

RolandWill: /* 19. One morning each member of Angela's family drank an eight-ounce cup of coffee and milk, with the (nonzero) amounts of coffee and milk varying from cup to cup. Angela drank a quarter of the total amount of milk and a sixth of the total amount o

{{Infobox MATH110 Groups
| group number = 18
| member 1 = [[User:ChouJuChen|Audrey Chen]]
| member 2 = [[User:SifatHasan|Sifat Hasan]]
| member 3 = [[User:CaitlinLastiwkaFarquharson|Caitlin Lastiwka-Farquharson]]
| member 4 = [[User:VictoriaWall|Victoria Wall]]
| member 5 = [[User:RolandWill|Roland Will]]
| member 6 =
}}

==Sub-Pages==

Basic Skills Project [http://wiki.ubc.ca/Course:MATH110/003/Groups/Group_18/Basic_Skills_Project]

==Homework due October 20th, 2010==

I created a page for our homework due tomorrow: [http://wiki.ubc.ca/Course:MATH110/003/Groups/Group_18/Homework_October_20th,_2010 http://wiki.ubc.ca/Course:MATH110/003/Groups/Group 18/Homework October 20th, 2010]

-Roland

I've moved the page, it was missing the ''Course:'' part which means it was created directly inside the wiki and not as a subpage of your group page, which is something the wiki admins don't like that much. By the way, you're allowed to use spaces in the name of your pages.

-- [[User:DavidKohler|DavidKohler]] 06:28, 20 October 2010 (UTC)

1-5

Victoria Wall

1.A bus traveled from the terminal to the airport at an average speed of 30 mi/hr and the trip took an hour and 20 min. The bus then traveled from the airport back to the terminal and again averaged 30 mi/hr. However, the return trip required 80 min. Explain.

' 'Lets call the terminal T and the airport A. If the bus travelled from T to A at 30mi/hr and it took them one hour and 20 mins to get from T to A at this speed, and there are 60 minutes in one hour, it took the bus 60min + 20min to get to A which is a total of 80min. The bus took 80 min to get from T to A. To get from A to T at the same speed (30mi/hr) it took the bus 80min. 80min = 80 min. This means going from A to T or vis versa at 30 mi/hr it will take the bus 80min.

2.A lady did not have her driver's license with her when she failed to stop at a stop sign and then went three blocks down a one-way street the wrong way. A policeman saw her, but he did not stop her. Explain.

' 'The lady was walking. It never says she was driving.

3.One of three boxes contains apples, another box contains oranges, and another box contains a mixture of apples and oranges. The boxes are labeled APPLES, ORANGES and APPLES AND ORANGES, but each label is incorrect. Can you select one fruit from only one box and determine the correct labels? Explain.

' 'if you selecet from the box APPLES AND ORANGES then you will be able to see the labels if they are correct or not.

4.I am the brother of the blind fiddler, but brothers I have none. How can this be?

' 'Since it says that he is the brother of the blind fiddler it does not mean that the fiddle is male, since he has no brothers than the fiddler must be a female.

5.Two quarters rest next to each other on a table. One coin is held fixed while the second coin is rolled around the edge of the first coin with no slipping. When the moving coin returns to its original position, how many times has it revolved?

' 'This is because the moving quarters revolves two full revolutions

6-10

Caitlin Lastiwka- Farquharson

6. Three kinds of apples are all mixed up in a basket. How many apples must you draw without (without looking) from the basket to be sure of getting at least two of a kind?

' ' To be sure you are getting at least two of a kind, you must select all of the other types of apples, plus two more. Meaning that only once you have selected all of the other apples can you be sure that you will select two of the kind you desire. It can be written like this: x,a x2, b and x3, c, with x representing the quantity of apples. This can be calculated by x2 + x3 +2. X2 representing one of the types of apples, x3 representing the other type and 2 representing 2 of the kind of apples you are trying to select. This is the only way to be sure you are getting at least two of a kind. ' '

7. Suppose you have 40 blue socks and 40 brown socks in a drawer. How many socks must you take from the drawer (without looking) to be sure of getting (i) a pair of the same colour, and (ii) a pair with different colors.

' 'You must take three socks from the drawer to ensure you have a pair that match. This is because if you only select two, one could be brown and one could be blue. Selecting three, ensures that at least two of them will be the same colour. As for part two, you would need to select 41 socks to ensure you had a pair of different coloured socks because if you select 40 or less you could get all the same colour, but selecting 41 ensures you will have at least one pair of mixed colour. ' '

8. Rueben says "Two days ago I was 20 years old. Later next year I will be 23 years old." Explain how this is possible.

' 'It is possible if your birthday is on the 31st of December and today is the 1st of January. This is because on the 30th of December (two days ago) you we’re 20 years old and now you are 21, later this year you will turn 22 on the 31st of December, and therefore 23 the next year.' '

9. A rope ladder hanging over the side of a boat has rungs one foot apart. Ten rungs are showing. If the tide rises five feet, how many rungs will be showing?

' ' 5 rungs will be showing, because if there are 10 showing now, and they are each a foot apart, then for 5 more rungs to be showing there would need to be an increase in the level of water by 5 feet. ' '

10.Suppose one-half of all people are chocolate eaters and one-half of all people are women. (i) Does it follow that one-fourth of all people are women chocolate eaters? (ii) Does it follow that one-half of all men are chocolate eaters? Explain.

' ' No, it does not follow that one-fourth of all people are women chocolate eaters and it does not follow that half of all men are chocolate eaters because are completely independent scenarios. Meaning that the the amount of women there are does not influence the amount of men that will eat chocolate. For example, If 50% of people are women and 50% of the entire population including men and women eat chocolate (arrived at by using the same logic that if 1/4 of women eat chocolate and 1/4 of men eat chocolate), that entire 50% could be comprised of women, meaning that no men eat chocolate disproving the statement.

11-14

Sifat Hasan

11. A woman, her older brother, her son, and her daughter are chess players. The worst player’s twin, who is one of the four players, and the best player are of opposite sex. The worst player and the best player have the same age. If this is possible, who is the worst player?

The four players (according to age, from oldest to youngest) are: woman's older brother, woman, and the son and the daughter (of the same age). Assuming that the children are of the same age (i.e. twins), the worst player is one of them, since they are the only ones who can have a twin. Assuming that the worst player is the daughter, her brother the son, is of the opposite sex as the woman, therefore the woman is the worst player. However, since the worst and the best player are of the same age, this is not possible, because the twins are of the opposite sex and they are of different genders.

12 A Manhattan fellow had a girlfriend in the Bronx and a girlfriend in Brooklyn. He decided which girlfriend to visit by arriving randomly at the train station and taking the first of the Bronx or Brooklyn trains that arrived. The trains to Brooklyn and the Bronx each arrived regularly every 10 minutes. Not long after he began his scheme the man's Bronx girlfriend left him because he rarely visited. Give a (logical) explanation

Assuming that the Bronx and the Brooklyn train arrive one after the other every 10 minutes, the only logical explanation would be that the man in Manhattan coincidentally went to the station 10 minutes or less before a train to Brooklyn arrived, most of the time.

13 If a clock takes 5 seconds to strike 5:00 (with 5 equally spaced chimes), how long does it take to strike 10:00 (with 10 equally spaced chimes)?

If it takes 5 seconds to strike 5, there will be 4 little halts in the middle. Therefore it takes 5 chimes 4 (5/4) = 1.25 second halts to finish. For 10 chimes, there are 9 halts so, it takes 9x 1.25 = 11.25 seconds for 10 halts.

14 One day in the maternity ward, the name tags for four girl babies became mixed up. (i) In how many different ways could two of the babies be tagged correctly and two of the babies be tagged incorrectly? (ii) In how many different ways could three of the babies be tagged correctly and one baby be tagged incorrectly?

(i)and (ii) If we take the babies names as A,B,C and D. There are 6 different combinations of the mix up, that two babies' names can be correct and 2 can be wrong. Assuming the name tags for the babies A,B,C and D are in respective order, they are ABDC, ADCB, ACBD, DBCA, CBAD and BACD. All other combinations for example BCAD will have one correct and 3 incorrect, or all four of them correct, because if 3 are correct, the fourth one has to be correct.

15-16

Roland Will

15. Alex says to you, “I'll bet you any amount of money that if I shuffle this deck of cards, there will always be as many red cards in the first half of the deck as there are black cards in the second half of the deck.” Should you accept his bet?

Answer: No, you shouldn't assuming the deck has equal amounts of red and black cards as in a standard 52 card deck.
Solution: In a standard 52 card deck, half of the cards (26) are black and half are red. If you take 26 cards at random from the deck, x of them will be black and y of them will be red, and x+y=26. As there are 26 of each color in the deck, then x+?=26 for the black cards in the deck and ?+y=26 for the red cards in the deck. As x+y=26 in the first randomly selected 26 cards, then the value of black cards in the other half of the deck must equal y, and the value of red cards in the other half of the deck must equal x meaning that "there will always be as many red cards in the first half of the deck as there are black cards in the second half of the deck."

16. Suppose that each daughter in your family has the same number of brothers as she has sisters, and each son in your family has twice as many sisters as he has brothers. How many sons and daughters are in the family?

Answer:3 total, 2 sister and 1 brother
Solution: Since the daughters in the family each have as many brothers as sisters the amount of sisters, with x standing for the amount of brothers, is x+1. As each brother has twice as many sisters as brothers, the amount of sisters must equal 2(x-1) or 2x-2. To find the number of brother: x+1=2x+1, 1=x-2, 3=x, which means that their are 3 brothers and 4 sisters (x+1= the number of sisters and x=3). This makes sense because a sister would have an equal amount of brothers to sisters, 3 sisters and 3 brothers, if there were 4 sisters and 3 brothers total, and each brother would have 4 sisters and 3 brothers, which is twice the amount of brothers to sisters.

17~21

Audrey Chen

17.The zero point on a bathroom scale is set incorrectly, but otherwise the scale is accurate. It shows 60 kg when Dan stands on the scale, 50 kg when Sarah stands on the scale, but 105 kg when Dan and Sarah both stand on the scale. Does the scale read too high or too low? Explain.

''The scale read too low, since Dan is shown as 60kg and Sarah is 50kg, suppose 60+50=110, 105-110=-5, so that means the scale is smaller than 0 in the beginning''

18. Alice takes one-third of the pennies from a large jar. Then Bret takes one-third of the remaining pennies from the jar. Finally, Carla takes one-third of the remaining pennies from the jar, leaving 40 pennies in the jar. How many pennies were in the jar at the start?

''If the total pennies is "x", Alice take 1/3x, so it has 2/3x left after Alice took it, than Bret take 1/3 out, after Alice took it, which is 2/3x*1/3= 2/9x, so in the beginning they have x, after Alice took it, it has 2/3x left, and Bret took 2/9x, so after Bret took it, it becomes 2/3x-2/9x= 4/9x-2/9x=2/9x left in the jar. Than Carla take 1/3 of the rest, so she took 1/3 of rest which is 2/9x*1/3=3/27x, so Alice took 1/3x, Bret tool 2/9x, Carla took 3/27x, three of them totaly took 1/3x+2/9x+3/27x=18/27x, so there still has x-18/27x= 9/27x= 1/3 left, 1/3x=40pennies, so x=120 pennies, so it was having 120 pennies in the jar.

19. One morning each member of Angela's family drank an eight-ounce cup of coffee and milk, with the (nonzero) amounts of coffee and milk varying from cup to cup. Angela drank a quarter of the total amount of milk and a sixth of the total amount of coffee. What is the least number of people in the family?

''If we let total milk is x, total coffee is y. Than 1/4x+1/6y=8, and because every cup is 8ounce, x+y is multiple by 8. So make it easier, we use 1/4x+1/6y=8 * 12 to both sides. than we will got 3x+2y=96, now we have 3x+2y=96 and x+y is multiple of 8, and the number that multiple by 8 is 8, 16, 24, 32... so 2x+2y= 16, 32, 48, 64, 80, 96, since 3x+2y=96, it can't be more than 96. It will only have 6 possible number, so if you take 3x+2y=96 substracting 2x+2y=16, 32, 48, 64, 80, 96 you can get 6 possible x, which are 80, 64, 48, 32, 16, and 0. Than put the number into 3x+2y=96, if you put 80 in, will get 20, which is bigger than 8, and also 64, 48. If we use 32, it will equal to 8, but that means we have 0 coffee, but coffee can't be 0, so there's only 16 and 0 left. Since Angela had 1/4 of total amount of milk, milk can't be 0. So we got 16ounce than 16*(1/4)=4, so that means she had 8-4=4 's coffee. So 4=1/6 coffee, than the total amount of coffee would be 4*6=24. than x=16 and y=24, 16+24=40 40/8ounce=5, so at least have 5 cups of drinks, so that means at least they have 5 members in Angela's family.''

==20.Of two clocks next to each other, one runs 5 min per hour fast and the other runs 5 min per hour slow. At midnight the clocks show the same time. At what time are they are one hour apart? ==

''Since one clock runs 5 min faster per hour, the other is 5 min slower, after clock runs an hour, two clocks will have 10 min different from each other. 60 min an hour. 60/10=6, so after 6 hours two clocks will having one hour apart, and that would be 6AM.''

==21.Sven placed exactly in the middle among all runners in a race. Dan was slower than Sven, in 10th place, and Lars was in 16th place. How many runners were in the race? ==

''There were 17 runners. Since lars was in 16th place, the runners at least have to be 16, than if Sven is placed exactly in the middle, it means it would have even number of runners. Because Dan is slower and he was at 10 place that tells us Seven has to be before 10th, and if there has 19 runners, Sven and Dan would be at the same place, so it should be 17 runners, than Sven would be at exactly in the middle which at 9th place.''

==22-25==

Roland Will

22. During a vacation, it rained on 13 days, but when it rained in the morning, the afternoon was sunny, and every rainy afternoon was preceded by a sunny morning. There were 11 sunny mornings and 12 sunny afternoons. How long was the vacation?

Answer: 18 days of vacation.

Solution: 13 of the days of vacation were half sunny and half rainy. As there were 23 sunny mornings and afternoons (11 sunny mornings+12 sunny afternoons = 23 sunny mornings and afternoons), 13 of those sunny afternoons or mornings were on half rainy days. This means there are 10 sunny half-days left over, which equal 5 sunny full days. The 5 sunny full days plus the 13 half sunny/rainy days equal 18 total days of vacation.

23. Suppose you overhear the following conversation: Paul: How old are your three children? Paula: The product of their ages is 36 and the sum of their ages is the same as today's date. Paul: That is not enough information. Paula: The oldest child also has red hair. If you were Paul could you determine the ages of Paula's children? Explain.

Answer: If I were Paul this might be possible, but since we don’t know the date that Paula said this, it is not possible for us to find out.

Solution: There are many different combinations of three numbers that can be multiplied and will produce 36. As we do not know the date that Paula said this, the only thing we can be sure of is that the sum of the ages is less than 31 because no month has more than 31 days. Unfortunately, only one set of ages (ages 1 year old, 1 year old and 36 years old) has a sum greater than 31, which leaves many possible combinations open as possible. For today’s date, the 13th, ages of 2, 2, and 9 would produce 36 and have a sum of 13, but, again, it is uncertain. If it were the first of the month, there would be no possible combinations that would produce 36 and sum 1.

24. Two candles of equal length were lit at the same time. One candle took 6 hr to burn out and the other candle took 3 hr to burn out. After how much time was one candle exactly twice as long as the other candle?

Answer: 2 hours.

Solution: The faster burning candle took half the time to burn as the slower burning candle (3 hours/ 6 hours = 1/2), meaning it burned twice as fast. This means that after 2/3 of the total burning time for the faster burning candle it will be 1/3 of its original height and at the slower burning candle will be at 2/3 of its original height and 1/3 is half of 2/3. Since the faster burning candle took 3 hours to burn, 2/3 of its total burning time is 2 hours.

25. Two candles of length L and L + 1 were lit at 6:00 and 4:30, respectively. At 8:30 they had the same length. The longer candle died at 10:30 and the shorter candle died at 10:00. Find L.

Answer: L=2.

Solution: The shorter candle lasted for 4 hours and the longer candle lasted for 6 hours. As 6 hours – 4 hours = 2 hours and 2 hours / 4 hours = 1/2, the longer candle lasted 50% longer and was, therefore, 50% longer in length. This means that the +1 in L+1 on the longer candle was 1/2 of L. 1/2L=1, so L=2*1, L=2.

Course:MATH110/Archive/2010-2011/003/Groups/Group 18

2010-11-12T05:27:23Z

RolandWill: /* 18. Alice takes one-third of the pennies from a large jar. Then Bret takes one-third of the remaining pennies from the jar. Finally, Carla takes one-third of the remaining pennies from the jar, leaving 40 pennies in the jar. How many pennies were

{{Infobox MATH110 Groups
| group number = 18
| member 1 = [[User:ChouJuChen|Audrey Chen]]
| member 2 = [[User:SifatHasan|Sifat Hasan]]
| member 3 = [[User:CaitlinLastiwkaFarquharson|Caitlin Lastiwka-Farquharson]]
| member 4 = [[User:VictoriaWall|Victoria Wall]]
| member 5 = [[User:RolandWill|Roland Will]]
| member 6 =
}}

==Sub-Pages==

Basic Skills Project [http://wiki.ubc.ca/Course:MATH110/003/Groups/Group_18/Basic_Skills_Project]

==Homework due October 20th, 2010==

I created a page for our homework due tomorrow: [http://wiki.ubc.ca/Course:MATH110/003/Groups/Group_18/Homework_October_20th,_2010 http://wiki.ubc.ca/Course:MATH110/003/Groups/Group 18/Homework October 20th, 2010]

-Roland

I've moved the page, it was missing the ''Course:'' part which means it was created directly inside the wiki and not as a subpage of your group page, which is something the wiki admins don't like that much. By the way, you're allowed to use spaces in the name of your pages.

-- [[User:DavidKohler|DavidKohler]] 06:28, 20 October 2010 (UTC)

1-5

Victoria Wall

1.A bus traveled from the terminal to the airport at an average speed of 30 mi/hr and the trip took an hour and 20 min. The bus then traveled from the airport back to the terminal and again averaged 30 mi/hr. However, the return trip required 80 min. Explain.

' 'Lets call the terminal T and the airport A. If the bus travelled from T to A at 30mi/hr and it took them one hour and 20 mins to get from T to A at this speed, and there are 60 minutes in one hour, it took the bus 60min + 20min to get to A which is a total of 80min. The bus took 80 min to get from T to A. To get from A to T at the same speed (30mi/hr) it took the bus 80min. 80min = 80 min. This means going from A to T or vis versa at 30 mi/hr it will take the bus 80min.

2.A lady did not have her driver's license with her when she failed to stop at a stop sign and then went three blocks down a one-way street the wrong way. A policeman saw her, but he did not stop her. Explain.

' 'The lady was walking. It never says she was driving.

3.One of three boxes contains apples, another box contains oranges, and another box contains a mixture of apples and oranges. The boxes are labeled APPLES, ORANGES and APPLES AND ORANGES, but each label is incorrect. Can you select one fruit from only one box and determine the correct labels? Explain.

' 'if you selecet from the box APPLES AND ORANGES then you will be able to see the labels if they are correct or not.

4.I am the brother of the blind fiddler, but brothers I have none. How can this be?

' 'Since it says that he is the brother of the blind fiddler it does not mean that the fiddle is male, since he has no brothers than the fiddler must be a female.

5.Two quarters rest next to each other on a table. One coin is held fixed while the second coin is rolled around the edge of the first coin with no slipping. When the moving coin returns to its original position, how many times has it revolved?

' 'This is because the moving quarters revolves two full revolutions

6-10

Caitlin Lastiwka- Farquharson

6. Three kinds of apples are all mixed up in a basket. How many apples must you draw without (without looking) from the basket to be sure of getting at least two of a kind?

' ' To be sure you are getting at least two of a kind, you must select all of the other types of apples, plus two more. Meaning that only once you have selected all of the other apples can you be sure that you will select two of the kind you desire. It can be written like this: x,a x2, b and x3, c, with x representing the quantity of apples. This can be calculated by x2 + x3 +2. X2 representing one of the types of apples, x3 representing the other type and 2 representing 2 of the kind of apples you are trying to select. This is the only way to be sure you are getting at least two of a kind. ' '

7. Suppose you have 40 blue socks and 40 brown socks in a drawer. How many socks must you take from the drawer (without looking) to be sure of getting (i) a pair of the same colour, and (ii) a pair with different colors.

' 'You must take three socks from the drawer to ensure you have a pair that match. This is because if you only select two, one could be brown and one could be blue. Selecting three, ensures that at least two of them will be the same colour. As for part two, you would need to select 41 socks to ensure you had a pair of different coloured socks because if you select 40 or less you could get all the same colour, but selecting 41 ensures you will have at least one pair of mixed colour. ' '

8. Rueben says "Two days ago I was 20 years old. Later next year I will be 23 years old." Explain how this is possible.

' 'It is possible if your birthday is on the 31st of December and today is the 1st of January. This is because on the 30th of December (two days ago) you we’re 20 years old and now you are 21, later this year you will turn 22 on the 31st of December, and therefore 23 the next year.' '

9. A rope ladder hanging over the side of a boat has rungs one foot apart. Ten rungs are showing. If the tide rises five feet, how many rungs will be showing?

' ' 5 rungs will be showing, because if there are 10 showing now, and they are each a foot apart, then for 5 more rungs to be showing there would need to be an increase in the level of water by 5 feet. ' '

10.Suppose one-half of all people are chocolate eaters and one-half of all people are women. (i) Does it follow that one-fourth of all people are women chocolate eaters? (ii) Does it follow that one-half of all men are chocolate eaters? Explain.

' ' No, it does not follow that one-fourth of all people are women chocolate eaters and it does not follow that half of all men are chocolate eaters because are completely independent scenarios. Meaning that the the amount of women there are does not influence the amount of men that will eat chocolate. For example, If 50% of people are women and 50% of the entire population including men and women eat chocolate (arrived at by using the same logic that if 1/4 of women eat chocolate and 1/4 of men eat chocolate), that entire 50% could be comprised of women, meaning that no men eat chocolate disproving the statement.

11-14

Sifat Hasan

11. A woman, her older brother, her son, and her daughter are chess players. The worst player’s twin, who is one of the four players, and the best player are of opposite sex. The worst player and the best player have the same age. If this is possible, who is the worst player?

The four players (according to age, from oldest to youngest) are: woman's older brother, woman, and the son and the daughter (of the same age). Assuming that the children are of the same age (i.e. twins), the worst player is one of them, since they are the only ones who can have a twin. Assuming that the worst player is the daughter, her brother the son, is of the opposite sex as the woman, therefore the woman is the worst player. However, since the worst and the best player are of the same age, this is not possible, because the twins are of the opposite sex and they are of different genders.

12 A Manhattan fellow had a girlfriend in the Bronx and a girlfriend in Brooklyn. He decided which girlfriend to visit by arriving randomly at the train station and taking the first of the Bronx or Brooklyn trains that arrived. The trains to Brooklyn and the Bronx each arrived regularly every 10 minutes. Not long after he began his scheme the man's Bronx girlfriend left him because he rarely visited. Give a (logical) explanation

Assuming that the Bronx and the Brooklyn train arrive one after the other every 10 minutes, the only logical explanation would be that the man in Manhattan coincidentally went to the station 10 minutes or less before a train to Brooklyn arrived, most of the time.

13 If a clock takes 5 seconds to strike 5:00 (with 5 equally spaced chimes), how long does it take to strike 10:00 (with 10 equally spaced chimes)?

If it takes 5 seconds to strike 5, there will be 4 little halts in the middle. Therefore it takes 5 chimes 4 (5/4) = 1.25 second halts to finish. For 10 chimes, there are 9 halts so, it takes 9x 1.25 = 11.25 seconds for 10 halts.

14 One day in the maternity ward, the name tags for four girl babies became mixed up. (i) In how many different ways could two of the babies be tagged correctly and two of the babies be tagged incorrectly? (ii) In how many different ways could three of the babies be tagged correctly and one baby be tagged incorrectly?

(i)and (ii) If we take the babies names as A,B,C and D. There are 6 different combinations of the mix up, that two babies' names can be correct and 2 can be wrong. Assuming the name tags for the babies A,B,C and D are in respective order, they are ABDC, ADCB, ACBD, DBCA, CBAD and BACD. All other combinations for example BCAD will have one correct and 3 incorrect, or all four of them correct, because if 3 are correct, the fourth one has to be correct.

15-16

Roland Will

15. Alex says to you, “I'll bet you any amount of money that if I shuffle this deck of cards, there will always be as many red cards in the first half of the deck as there are black cards in the second half of the deck.” Should you accept his bet?

Answer: No, you shouldn't assuming the deck has equal amounts of red and black cards as in a standard 52 card deck.
Solution: In a standard 52 card deck, half of the cards (26) are black and half are red. If you take 26 cards at random from the deck, x of them will be black and y of them will be red, and x+y=26. As there are 26 of each color in the deck, then x+?=26 for the black cards in the deck and ?+y=26 for the red cards in the deck. As x+y=26 in the first randomly selected 26 cards, then the value of black cards in the other half of the deck must equal y, and the value of red cards in the other half of the deck must equal x meaning that "there will always be as many red cards in the first half of the deck as there are black cards in the second half of the deck."

16. Suppose that each daughter in your family has the same number of brothers as she has sisters, and each son in your family has twice as many sisters as he has brothers. How many sons and daughters are in the family?

Answer:3 total, 2 sister and 1 brother
Solution: Since the daughters in the family each have as many brothers as sisters the amount of sisters, with x standing for the amount of brothers, is x+1. As each brother has twice as many sisters as brothers, the amount of sisters must equal 2(x-1) or 2x-2. To find the number of brother: x+1=2x+1, 1=x-2, 3=x, which means that their are 3 brothers and 4 sisters (x+1= the number of sisters and x=3). This makes sense because a sister would have an equal amount of brothers to sisters, 3 sisters and 3 brothers, if there were 4 sisters and 3 brothers total, and each brother would have 4 sisters and 3 brothers, which is twice the amount of brothers to sisters.

17~21

Audrey Chen

17.The zero point on a bathroom scale is set incorrectly, but otherwise the scale is accurate. It shows 60 kg when Dan stands on the scale, 50 kg when Sarah stands on the scale, but 105 kg when Dan and Sarah both stand on the scale. Does the scale read too high or too low? Explain.

''The scale read too low, since Dan is shown as 60kg and Sarah is 50kg, suppose 60+50=110, 105-110=-5, so that means the scale is smaller than 0 in the beginning''

18. Alice takes one-third of the pennies from a large jar. Then Bret takes one-third of the remaining pennies from the jar. Finally, Carla takes one-third of the remaining pennies from the jar, leaving 40 pennies in the jar. How many pennies were in the jar at the start?

''If the total pennies is "x", Alice take 1/3x, so it has 2/3x left after Alice took it, than Bret take 1/3 out, after Alice took it, which is 2/3x*1/3= 2/9x, so in the beginning they have x, after Alice took it, it has 2/3x left, and Bret took 2/9x, so after Bret took it, it becomes 2/3x-2/9x= 4/9x-2/9x=2/9x left in the jar. Than Carla take 1/3 of the rest, so she took 1/3 of rest which is 2/9x*1/3=3/27x, so Alice took 1/3x, Bret tool 2/9x, Carla took 3/27x, three of them totaly took 1/3x+2/9x+3/27x=18/27x, so there still has x-18/27x= 9/27x= 1/3 left, 1/3x=40pennies, so x=120 pennies, so it was having 120 pennies in the jar.

==19. One morning each member of Angela's family drank an eight-ounce cup of coffee and milk, with the (nonzero) amounts of coffee and milk varying from cup to cup. Angela drank a quarter of the total amount of milk and a sixth of the total amount of coffee. What is the least number of people in the family? ==

''If we let total milk is x, total coffee is y. Than 1/4x+1/6y=8, and because every cup is 8ounce, x+y is multiple by 8. So make it easier, we use 1/4x+1/6y=8 * 12 to both sides. than we will got 3x+2y=96, now we have 3x+2y=96 and x+y is multiple of 8, and the number that multiple by 8 is 8, 16, 24, 32... so 2x+2y= 16, 32, 48, 64, 80, 96, since 3x+2y=96, it can't be more than 96. It will only have 6 possible number, so if you take 3x+2y=96 substracting 2x+2y=16, 32, 48, 64, 80, 96 you can get 6 possible x, which are 80, 64, 48, 32, 16, and 0. Than put the number into 3x+2y=96, if you put 80 in, will get 20, which is bigger than 8, and also 64, 48. If we use 32, it will equal to 8, but that means we have 0 coffee, but coffee can't be 0, so there's only 16 and 0 left. Since Angela had 1/4 of total amount of milk, milk can't be 0. So we got 16ounce than 16*(1/4)=4, so that means she had 8-4=4 's coffee. So 4=1/6 coffee, than the total amount of coffee would be 4*6=24. than x=16 and y=24, 16+24=40 40/8ounce=5, so at least have 5 cups of drinks, so that means at least they have 5 members in Angela's family.''

==20.Of two clocks next to each other, one runs 5 min per hour fast and the other runs 5 min per hour slow. At midnight the clocks show the same time. At what time are they are one hour apart? ==

''Since one clock runs 5 min faster per hour, the other is 5 min slower, after clock runs an hour, two clocks will have 10 min different from each other. 60 min an hour. 60/10=6, so after 6 hours two clocks will having one hour apart, and that would be 6AM.''

==21.Sven placed exactly in the middle among all runners in a race. Dan was slower than Sven, in 10th place, and Lars was in 16th place. How many runners were in the race? ==

''There were 17 runners. Since lars was in 16th place, the runners at least have to be 16, than if Sven is placed exactly in the middle, it means it would have even number of runners. Because Dan is slower and he was at 10 place that tells us Seven has to be before 10th, and if there has 19 runners, Sven and Dan would be at the same place, so it should be 17 runners, than Sven would be at exactly in the middle which at 9th place.''

==22-25==

Roland Will

22. During a vacation, it rained on 13 days, but when it rained in the morning, the afternoon was sunny, and every rainy afternoon was preceded by a sunny morning. There were 11 sunny mornings and 12 sunny afternoons. How long was the vacation?

Answer: 18 days of vacation.

Solution: 13 of the days of vacation were half sunny and half rainy. As there were 23 sunny mornings and afternoons (11 sunny mornings+12 sunny afternoons = 23 sunny mornings and afternoons), 13 of those sunny afternoons or mornings were on half rainy days. This means there are 10 sunny half-days left over, which equal 5 sunny full days. The 5 sunny full days plus the 13 half sunny/rainy days equal 18 total days of vacation.

23. Suppose you overhear the following conversation: Paul: How old are your three children? Paula: The product of their ages is 36 and the sum of their ages is the same as today's date. Paul: That is not enough information. Paula: The oldest child also has red hair. If you were Paul could you determine the ages of Paula's children? Explain.

Answer: If I were Paul this might be possible, but since we don’t know the date that Paula said this, it is not possible for us to find out.

Solution: There are many different combinations of three numbers that can be multiplied and will produce 36. As we do not know the date that Paula said this, the only thing we can be sure of is that the sum of the ages is less than 31 because no month has more than 31 days. Unfortunately, only one set of ages (ages 1 year old, 1 year old and 36 years old) has a sum greater than 31, which leaves many possible combinations open as possible. For today’s date, the 13th, ages of 2, 2, and 9 would produce 36 and have a sum of 13, but, again, it is uncertain. If it were the first of the month, there would be no possible combinations that would produce 36 and sum 1.

24. Two candles of equal length were lit at the same time. One candle took 6 hr to burn out and the other candle took 3 hr to burn out. After how much time was one candle exactly twice as long as the other candle?

Answer: 2 hours.

Solution: The faster burning candle took half the time to burn as the slower burning candle (3 hours/ 6 hours = 1/2), meaning it burned twice as fast. This means that after 2/3 of the total burning time for the faster burning candle it will be 1/3 of its original height and at the slower burning candle will be at 2/3 of its original height and 1/3 is half of 2/3. Since the faster burning candle took 3 hours to burn, 2/3 of its total burning time is 2 hours.

25. Two candles of length L and L + 1 were lit at 6:00 and 4:30, respectively. At 8:30 they had the same length. The longer candle died at 10:30 and the shorter candle died at 10:00. Find L.

Answer: L=2.

Solution: The shorter candle lasted for 4 hours and the longer candle lasted for 6 hours. As 6 hours – 4 hours = 2 hours and 2 hours / 4 hours = 1/2, the longer candle lasted 50% longer and was, therefore, 50% longer in length. This means that the +1 in L+1 on the longer candle was 1/2 of L. 1/2L=1, so L=2*1, L=2.

Course:MATH110/Archive/2010-2011/003/Groups/Group 18

2010-11-12T05:27:11Z

RolandWill: /* 17.The zero point on a bathroom scale is set incorrectly, but otherwise the scale is accurate. It shows 60 kg when Dan stands on the scale, 50 kg when Sarah stands on the scale, but 105 kg when Dan and Sarah both stand on the scale. Does the scale

{{Infobox MATH110 Groups
| group number = 18
| member 1 = [[User:ChouJuChen|Audrey Chen]]
| member 2 = [[User:SifatHasan|Sifat Hasan]]
| member 3 = [[User:CaitlinLastiwkaFarquharson|Caitlin Lastiwka-Farquharson]]
| member 4 = [[User:VictoriaWall|Victoria Wall]]
| member 5 = [[User:RolandWill|Roland Will]]
| member 6 =
}}

==Sub-Pages==

Basic Skills Project [http://wiki.ubc.ca/Course:MATH110/003/Groups/Group_18/Basic_Skills_Project]

==Homework due October 20th, 2010==

I created a page for our homework due tomorrow: [http://wiki.ubc.ca/Course:MATH110/003/Groups/Group_18/Homework_October_20th,_2010 http://wiki.ubc.ca/Course:MATH110/003/Groups/Group 18/Homework October 20th, 2010]

-Roland

I've moved the page, it was missing the ''Course:'' part which means it was created directly inside the wiki and not as a subpage of your group page, which is something the wiki admins don't like that much. By the way, you're allowed to use spaces in the name of your pages.

-- [[User:DavidKohler|DavidKohler]] 06:28, 20 October 2010 (UTC)

1-5

Victoria Wall

1.A bus traveled from the terminal to the airport at an average speed of 30 mi/hr and the trip took an hour and 20 min. The bus then traveled from the airport back to the terminal and again averaged 30 mi/hr. However, the return trip required 80 min. Explain.

' 'Lets call the terminal T and the airport A. If the bus travelled from T to A at 30mi/hr and it took them one hour and 20 mins to get from T to A at this speed, and there are 60 minutes in one hour, it took the bus 60min + 20min to get to A which is a total of 80min. The bus took 80 min to get from T to A. To get from A to T at the same speed (30mi/hr) it took the bus 80min. 80min = 80 min. This means going from A to T or vis versa at 30 mi/hr it will take the bus 80min.

2.A lady did not have her driver's license with her when she failed to stop at a stop sign and then went three blocks down a one-way street the wrong way. A policeman saw her, but he did not stop her. Explain.

' 'The lady was walking. It never says she was driving.

3.One of three boxes contains apples, another box contains oranges, and another box contains a mixture of apples and oranges. The boxes are labeled APPLES, ORANGES and APPLES AND ORANGES, but each label is incorrect. Can you select one fruit from only one box and determine the correct labels? Explain.

' 'if you selecet from the box APPLES AND ORANGES then you will be able to see the labels if they are correct or not.

4.I am the brother of the blind fiddler, but brothers I have none. How can this be?

' 'Since it says that he is the brother of the blind fiddler it does not mean that the fiddle is male, since he has no brothers than the fiddler must be a female.

5.Two quarters rest next to each other on a table. One coin is held fixed while the second coin is rolled around the edge of the first coin with no slipping. When the moving coin returns to its original position, how many times has it revolved?

' 'This is because the moving quarters revolves two full revolutions

6-10

Caitlin Lastiwka- Farquharson

6. Three kinds of apples are all mixed up in a basket. How many apples must you draw without (without looking) from the basket to be sure of getting at least two of a kind?

' ' To be sure you are getting at least two of a kind, you must select all of the other types of apples, plus two more. Meaning that only once you have selected all of the other apples can you be sure that you will select two of the kind you desire. It can be written like this: x,a x2, b and x3, c, with x representing the quantity of apples. This can be calculated by x2 + x3 +2. X2 representing one of the types of apples, x3 representing the other type and 2 representing 2 of the kind of apples you are trying to select. This is the only way to be sure you are getting at least two of a kind. ' '

7. Suppose you have 40 blue socks and 40 brown socks in a drawer. How many socks must you take from the drawer (without looking) to be sure of getting (i) a pair of the same colour, and (ii) a pair with different colors.

' 'You must take three socks from the drawer to ensure you have a pair that match. This is because if you only select two, one could be brown and one could be blue. Selecting three, ensures that at least two of them will be the same colour. As for part two, you would need to select 41 socks to ensure you had a pair of different coloured socks because if you select 40 or less you could get all the same colour, but selecting 41 ensures you will have at least one pair of mixed colour. ' '

8. Rueben says "Two days ago I was 20 years old. Later next year I will be 23 years old." Explain how this is possible.

' 'It is possible if your birthday is on the 31st of December and today is the 1st of January. This is because on the 30th of December (two days ago) you we’re 20 years old and now you are 21, later this year you will turn 22 on the 31st of December, and therefore 23 the next year.' '

9. A rope ladder hanging over the side of a boat has rungs one foot apart. Ten rungs are showing. If the tide rises five feet, how many rungs will be showing?

' ' 5 rungs will be showing, because if there are 10 showing now, and they are each a foot apart, then for 5 more rungs to be showing there would need to be an increase in the level of water by 5 feet. ' '

10.Suppose one-half of all people are chocolate eaters and one-half of all people are women. (i) Does it follow that one-fourth of all people are women chocolate eaters? (ii) Does it follow that one-half of all men are chocolate eaters? Explain.

' ' No, it does not follow that one-fourth of all people are women chocolate eaters and it does not follow that half of all men are chocolate eaters because are completely independent scenarios. Meaning that the the amount of women there are does not influence the amount of men that will eat chocolate. For example, If 50% of people are women and 50% of the entire population including men and women eat chocolate (arrived at by using the same logic that if 1/4 of women eat chocolate and 1/4 of men eat chocolate), that entire 50% could be comprised of women, meaning that no men eat chocolate disproving the statement.

11-14

Sifat Hasan

11. A woman, her older brother, her son, and her daughter are chess players. The worst player’s twin, who is one of the four players, and the best player are of opposite sex. The worst player and the best player have the same age. If this is possible, who is the worst player?

The four players (according to age, from oldest to youngest) are: woman's older brother, woman, and the son and the daughter (of the same age). Assuming that the children are of the same age (i.e. twins), the worst player is one of them, since they are the only ones who can have a twin. Assuming that the worst player is the daughter, her brother the son, is of the opposite sex as the woman, therefore the woman is the worst player. However, since the worst and the best player are of the same age, this is not possible, because the twins are of the opposite sex and they are of different genders.

12 A Manhattan fellow had a girlfriend in the Bronx and a girlfriend in Brooklyn. He decided which girlfriend to visit by arriving randomly at the train station and taking the first of the Bronx or Brooklyn trains that arrived. The trains to Brooklyn and the Bronx each arrived regularly every 10 minutes. Not long after he began his scheme the man's Bronx girlfriend left him because he rarely visited. Give a (logical) explanation

Assuming that the Bronx and the Brooklyn train arrive one after the other every 10 minutes, the only logical explanation would be that the man in Manhattan coincidentally went to the station 10 minutes or less before a train to Brooklyn arrived, most of the time.

13 If a clock takes 5 seconds to strike 5:00 (with 5 equally spaced chimes), how long does it take to strike 10:00 (with 10 equally spaced chimes)?

If it takes 5 seconds to strike 5, there will be 4 little halts in the middle. Therefore it takes 5 chimes 4 (5/4) = 1.25 second halts to finish. For 10 chimes, there are 9 halts so, it takes 9x 1.25 = 11.25 seconds for 10 halts.

14 One day in the maternity ward, the name tags for four girl babies became mixed up. (i) In how many different ways could two of the babies be tagged correctly and two of the babies be tagged incorrectly? (ii) In how many different ways could three of the babies be tagged correctly and one baby be tagged incorrectly?

(i)and (ii) If we take the babies names as A,B,C and D. There are 6 different combinations of the mix up, that two babies' names can be correct and 2 can be wrong. Assuming the name tags for the babies A,B,C and D are in respective order, they are ABDC, ADCB, ACBD, DBCA, CBAD and BACD. All other combinations for example BCAD will have one correct and 3 incorrect, or all four of them correct, because if 3 are correct, the fourth one has to be correct.

15-16

Roland Will

15. Alex says to you, “I'll bet you any amount of money that if I shuffle this deck of cards, there will always be as many red cards in the first half of the deck as there are black cards in the second half of the deck.” Should you accept his bet?

Answer: No, you shouldn't assuming the deck has equal amounts of red and black cards as in a standard 52 card deck.
Solution: In a standard 52 card deck, half of the cards (26) are black and half are red. If you take 26 cards at random from the deck, x of them will be black and y of them will be red, and x+y=26. As there are 26 of each color in the deck, then x+?=26 for the black cards in the deck and ?+y=26 for the red cards in the deck. As x+y=26 in the first randomly selected 26 cards, then the value of black cards in the other half of the deck must equal y, and the value of red cards in the other half of the deck must equal x meaning that "there will always be as many red cards in the first half of the deck as there are black cards in the second half of the deck."

16. Suppose that each daughter in your family has the same number of brothers as she has sisters, and each son in your family has twice as many sisters as he has brothers. How many sons and daughters are in the family?

Answer:3 total, 2 sister and 1 brother
Solution: Since the daughters in the family each have as many brothers as sisters the amount of sisters, with x standing for the amount of brothers, is x+1. As each brother has twice as many sisters as brothers, the amount of sisters must equal 2(x-1) or 2x-2. To find the number of brother: x+1=2x+1, 1=x-2, 3=x, which means that their are 3 brothers and 4 sisters (x+1= the number of sisters and x=3). This makes sense because a sister would have an equal amount of brothers to sisters, 3 sisters and 3 brothers, if there were 4 sisters and 3 brothers total, and each brother would have 4 sisters and 3 brothers, which is twice the amount of brothers to sisters.

17~21

Audrey Chen

17.The zero point on a bathroom scale is set incorrectly, but otherwise the scale is accurate. It shows 60 kg when Dan stands on the scale, 50 kg when Sarah stands on the scale, but 105 kg when Dan and Sarah both stand on the scale. Does the scale read too high or too low? Explain.

''The scale read too low, since Dan is shown as 60kg and Sarah is 50kg, suppose 60+50=110, 105-110=-5, so that means the scale is smaller than 0 in the beginning''

==18. Alice takes one-third of the pennies from a large jar. Then Bret takes one-third of the remaining pennies from the jar. Finally, Carla takes one-third of the remaining pennies from the jar, leaving 40 pennies in the jar. How many pennies were in the jar at the start? ==

''If the total pennies is "x", Alice take 1/3x, so it has 2/3x left after Alice took it, than Bret take 1/3 out, after Alice took it, which is 2/3x*1/3= 2/9x, so in the beginning they have x, after Alice took it, it has 2/3x left, and Bret took 2/9x, so after Bret took it, it becomes 2/3x-2/9x= 4/9x-2/9x=2/9x left in the jar. Than Carla take 1/3 of the rest, so she took 1/3 of rest which is 2/9x*1/3=3/27x, so Alice took 1/3x, Bret tool 2/9x, Carla took 3/27x, three of them totaly took 1/3x+2/9x+3/27x=18/27x, so there still has x-18/27x= 9/27x= 1/3 left, 1/3x=40pennies, so x=120 pennies, so it was having 120 pennies in the jar.

==19. One morning each member of Angela's family drank an eight-ounce cup of coffee and milk, with the (nonzero) amounts of coffee and milk varying from cup to cup. Angela drank a quarter of the total amount of milk and a sixth of the total amount of coffee. What is the least number of people in the family? ==

''If we let total milk is x, total coffee is y. Than 1/4x+1/6y=8, and because every cup is 8ounce, x+y is multiple by 8. So make it easier, we use 1/4x+1/6y=8 * 12 to both sides. than we will got 3x+2y=96, now we have 3x+2y=96 and x+y is multiple of 8, and the number that multiple by 8 is 8, 16, 24, 32... so 2x+2y= 16, 32, 48, 64, 80, 96, since 3x+2y=96, it can't be more than 96. It will only have 6 possible number, so if you take 3x+2y=96 substracting 2x+2y=16, 32, 48, 64, 80, 96 you can get 6 possible x, which are 80, 64, 48, 32, 16, and 0. Than put the number into 3x+2y=96, if you put 80 in, will get 20, which is bigger than 8, and also 64, 48. If we use 32, it will equal to 8, but that means we have 0 coffee, but coffee can't be 0, so there's only 16 and 0 left. Since Angela had 1/4 of total amount of milk, milk can't be 0. So we got 16ounce than 16*(1/4)=4, so that means she had 8-4=4 's coffee. So 4=1/6 coffee, than the total amount of coffee would be 4*6=24. than x=16 and y=24, 16+24=40 40/8ounce=5, so at least have 5 cups of drinks, so that means at least they have 5 members in Angela's family.''

==20.Of two clocks next to each other, one runs 5 min per hour fast and the other runs 5 min per hour slow. At midnight the clocks show the same time. At what time are they are one hour apart? ==

''Since one clock runs 5 min faster per hour, the other is 5 min slower, after clock runs an hour, two clocks will have 10 min different from each other. 60 min an hour. 60/10=6, so after 6 hours two clocks will having one hour apart, and that would be 6AM.''

==21.Sven placed exactly in the middle among all runners in a race. Dan was slower than Sven, in 10th place, and Lars was in 16th place. How many runners were in the race? ==

''There were 17 runners. Since lars was in 16th place, the runners at least have to be 16, than if Sven is placed exactly in the middle, it means it would have even number of runners. Because Dan is slower and he was at 10 place that tells us Seven has to be before 10th, and if there has 19 runners, Sven and Dan would be at the same place, so it should be 17 runners, than Sven would be at exactly in the middle which at 9th place.''

==22-25==

Roland Will

22. During a vacation, it rained on 13 days, but when it rained in the morning, the afternoon was sunny, and every rainy afternoon was preceded by a sunny morning. There were 11 sunny mornings and 12 sunny afternoons. How long was the vacation?

Answer: 18 days of vacation.

Solution: 13 of the days of vacation were half sunny and half rainy. As there were 23 sunny mornings and afternoons (11 sunny mornings+12 sunny afternoons = 23 sunny mornings and afternoons), 13 of those sunny afternoons or mornings were on half rainy days. This means there are 10 sunny half-days left over, which equal 5 sunny full days. The 5 sunny full days plus the 13 half sunny/rainy days equal 18 total days of vacation.

23. Suppose you overhear the following conversation: Paul: How old are your three children? Paula: The product of their ages is 36 and the sum of their ages is the same as today's date. Paul: That is not enough information. Paula: The oldest child also has red hair. If you were Paul could you determine the ages of Paula's children? Explain.

Answer: If I were Paul this might be possible, but since we don’t know the date that Paula said this, it is not possible for us to find out.

Solution: There are many different combinations of three numbers that can be multiplied and will produce 36. As we do not know the date that Paula said this, the only thing we can be sure of is that the sum of the ages is less than 31 because no month has more than 31 days. Unfortunately, only one set of ages (ages 1 year old, 1 year old and 36 years old) has a sum greater than 31, which leaves many possible combinations open as possible. For today’s date, the 13th, ages of 2, 2, and 9 would produce 36 and have a sum of 13, but, again, it is uncertain. If it were the first of the month, there would be no possible combinations that would produce 36 and sum 1.

24. Two candles of equal length were lit at the same time. One candle took 6 hr to burn out and the other candle took 3 hr to burn out. After how much time was one candle exactly twice as long as the other candle?

Answer: 2 hours.

Solution: The faster burning candle took half the time to burn as the slower burning candle (3 hours/ 6 hours = 1/2), meaning it burned twice as fast. This means that after 2/3 of the total burning time for the faster burning candle it will be 1/3 of its original height and at the slower burning candle will be at 2/3 of its original height and 1/3 is half of 2/3. Since the faster burning candle took 3 hours to burn, 2/3 of its total burning time is 2 hours.

25. Two candles of length L and L + 1 were lit at 6:00 and 4:30, respectively. At 8:30 they had the same length. The longer candle died at 10:30 and the shorter candle died at 10:00. Find L.

Answer: L=2.

Solution: The shorter candle lasted for 4 hours and the longer candle lasted for 6 hours. As 6 hours – 4 hours = 2 hours and 2 hours / 4 hours = 1/2, the longer candle lasted 50% longer and was, therefore, 50% longer in length. This means that the +1 in L+1 on the longer candle was 1/2 of L. 1/2L=1, so L=2*1, L=2.

Course:MATH110/Archive/2010-2011/003/Groups/Group 18

2010-11-12T05:26:56Z

RolandWill: /* Audrey Chen */

{{Infobox MATH110 Groups
| group number = 18
| member 1 = [[User:ChouJuChen|Audrey Chen]]
| member 2 = [[User:SifatHasan|Sifat Hasan]]
| member 3 = [[User:CaitlinLastiwkaFarquharson|Caitlin Lastiwka-Farquharson]]
| member 4 = [[User:VictoriaWall|Victoria Wall]]
| member 5 = [[User:RolandWill|Roland Will]]
| member 6 =
}}

==Sub-Pages==

Basic Skills Project [http://wiki.ubc.ca/Course:MATH110/003/Groups/Group_18/Basic_Skills_Project]

==Homework due October 20th, 2010==

I created a page for our homework due tomorrow: [http://wiki.ubc.ca/Course:MATH110/003/Groups/Group_18/Homework_October_20th,_2010 http://wiki.ubc.ca/Course:MATH110/003/Groups/Group 18/Homework October 20th, 2010]

-Roland

I've moved the page, it was missing the ''Course:'' part which means it was created directly inside the wiki and not as a subpage of your group page, which is something the wiki admins don't like that much. By the way, you're allowed to use spaces in the name of your pages.

-- [[User:DavidKohler|DavidKohler]] 06:28, 20 October 2010 (UTC)

1-5

Victoria Wall

1.A bus traveled from the terminal to the airport at an average speed of 30 mi/hr and the trip took an hour and 20 min. The bus then traveled from the airport back to the terminal and again averaged 30 mi/hr. However, the return trip required 80 min. Explain.

' 'Lets call the terminal T and the airport A. If the bus travelled from T to A at 30mi/hr and it took them one hour and 20 mins to get from T to A at this speed, and there are 60 minutes in one hour, it took the bus 60min + 20min to get to A which is a total of 80min. The bus took 80 min to get from T to A. To get from A to T at the same speed (30mi/hr) it took the bus 80min. 80min = 80 min. This means going from A to T or vis versa at 30 mi/hr it will take the bus 80min.

2.A lady did not have her driver's license with her when she failed to stop at a stop sign and then went three blocks down a one-way street the wrong way. A policeman saw her, but he did not stop her. Explain.

' 'The lady was walking. It never says she was driving.

3.One of three boxes contains apples, another box contains oranges, and another box contains a mixture of apples and oranges. The boxes are labeled APPLES, ORANGES and APPLES AND ORANGES, but each label is incorrect. Can you select one fruit from only one box and determine the correct labels? Explain.

' 'if you selecet from the box APPLES AND ORANGES then you will be able to see the labels if they are correct or not.

4.I am the brother of the blind fiddler, but brothers I have none. How can this be?

' 'Since it says that he is the brother of the blind fiddler it does not mean that the fiddle is male, since he has no brothers than the fiddler must be a female.

5.Two quarters rest next to each other on a table. One coin is held fixed while the second coin is rolled around the edge of the first coin with no slipping. When the moving coin returns to its original position, how many times has it revolved?

' 'This is because the moving quarters revolves two full revolutions

6-10

Caitlin Lastiwka- Farquharson

6. Three kinds of apples are all mixed up in a basket. How many apples must you draw without (without looking) from the basket to be sure of getting at least two of a kind?

' ' To be sure you are getting at least two of a kind, you must select all of the other types of apples, plus two more. Meaning that only once you have selected all of the other apples can you be sure that you will select two of the kind you desire. It can be written like this: x,a x2, b and x3, c, with x representing the quantity of apples. This can be calculated by x2 + x3 +2. X2 representing one of the types of apples, x3 representing the other type and 2 representing 2 of the kind of apples you are trying to select. This is the only way to be sure you are getting at least two of a kind. ' '

7. Suppose you have 40 blue socks and 40 brown socks in a drawer. How many socks must you take from the drawer (without looking) to be sure of getting (i) a pair of the same colour, and (ii) a pair with different colors.

' 'You must take three socks from the drawer to ensure you have a pair that match. This is because if you only select two, one could be brown and one could be blue. Selecting three, ensures that at least two of them will be the same colour. As for part two, you would need to select 41 socks to ensure you had a pair of different coloured socks because if you select 40 or less you could get all the same colour, but selecting 41 ensures you will have at least one pair of mixed colour. ' '

8. Rueben says "Two days ago I was 20 years old. Later next year I will be 23 years old." Explain how this is possible.

' 'It is possible if your birthday is on the 31st of December and today is the 1st of January. This is because on the 30th of December (two days ago) you we’re 20 years old and now you are 21, later this year you will turn 22 on the 31st of December, and therefore 23 the next year.' '

9. A rope ladder hanging over the side of a boat has rungs one foot apart. Ten rungs are showing. If the tide rises five feet, how many rungs will be showing?

' ' 5 rungs will be showing, because if there are 10 showing now, and they are each a foot apart, then for 5 more rungs to be showing there would need to be an increase in the level of water by 5 feet. ' '

10.Suppose one-half of all people are chocolate eaters and one-half of all people are women. (i) Does it follow that one-fourth of all people are women chocolate eaters? (ii) Does it follow that one-half of all men are chocolate eaters? Explain.

' ' No, it does not follow that one-fourth of all people are women chocolate eaters and it does not follow that half of all men are chocolate eaters because are completely independent scenarios. Meaning that the the amount of women there are does not influence the amount of men that will eat chocolate. For example, If 50% of people are women and 50% of the entire population including men and women eat chocolate (arrived at by using the same logic that if 1/4 of women eat chocolate and 1/4 of men eat chocolate), that entire 50% could be comprised of women, meaning that no men eat chocolate disproving the statement.

11-14

Sifat Hasan

11. A woman, her older brother, her son, and her daughter are chess players. The worst player’s twin, who is one of the four players, and the best player are of opposite sex. The worst player and the best player have the same age. If this is possible, who is the worst player?

The four players (according to age, from oldest to youngest) are: woman's older brother, woman, and the son and the daughter (of the same age). Assuming that the children are of the same age (i.e. twins), the worst player is one of them, since they are the only ones who can have a twin. Assuming that the worst player is the daughter, her brother the son, is of the opposite sex as the woman, therefore the woman is the worst player. However, since the worst and the best player are of the same age, this is not possible, because the twins are of the opposite sex and they are of different genders.

12 A Manhattan fellow had a girlfriend in the Bronx and a girlfriend in Brooklyn. He decided which girlfriend to visit by arriving randomly at the train station and taking the first of the Bronx or Brooklyn trains that arrived. The trains to Brooklyn and the Bronx each arrived regularly every 10 minutes. Not long after he began his scheme the man's Bronx girlfriend left him because he rarely visited. Give a (logical) explanation

Assuming that the Bronx and the Brooklyn train arrive one after the other every 10 minutes, the only logical explanation would be that the man in Manhattan coincidentally went to the station 10 minutes or less before a train to Brooklyn arrived, most of the time.

13 If a clock takes 5 seconds to strike 5:00 (with 5 equally spaced chimes), how long does it take to strike 10:00 (with 10 equally spaced chimes)?

If it takes 5 seconds to strike 5, there will be 4 little halts in the middle. Therefore it takes 5 chimes 4 (5/4) = 1.25 second halts to finish. For 10 chimes, there are 9 halts so, it takes 9x 1.25 = 11.25 seconds for 10 halts.

14 One day in the maternity ward, the name tags for four girl babies became mixed up. (i) In how many different ways could two of the babies be tagged correctly and two of the babies be tagged incorrectly? (ii) In how many different ways could three of the babies be tagged correctly and one baby be tagged incorrectly?

(i)and (ii) If we take the babies names as A,B,C and D. There are 6 different combinations of the mix up, that two babies' names can be correct and 2 can be wrong. Assuming the name tags for the babies A,B,C and D are in respective order, they are ABDC, ADCB, ACBD, DBCA, CBAD and BACD. All other combinations for example BCAD will have one correct and 3 incorrect, or all four of them correct, because if 3 are correct, the fourth one has to be correct.

15-16

Roland Will

15. Alex says to you, “I'll bet you any amount of money that if I shuffle this deck of cards, there will always be as many red cards in the first half of the deck as there are black cards in the second half of the deck.” Should you accept his bet?

Answer: No, you shouldn't assuming the deck has equal amounts of red and black cards as in a standard 52 card deck.
Solution: In a standard 52 card deck, half of the cards (26) are black and half are red. If you take 26 cards at random from the deck, x of them will be black and y of them will be red, and x+y=26. As there are 26 of each color in the deck, then x+?=26 for the black cards in the deck and ?+y=26 for the red cards in the deck. As x+y=26 in the first randomly selected 26 cards, then the value of black cards in the other half of the deck must equal y, and the value of red cards in the other half of the deck must equal x meaning that "there will always be as many red cards in the first half of the deck as there are black cards in the second half of the deck."

16. Suppose that each daughter in your family has the same number of brothers as she has sisters, and each son in your family has twice as many sisters as he has brothers. How many sons and daughters are in the family?

Answer:3 total, 2 sister and 1 brother
Solution: Since the daughters in the family each have as many brothers as sisters the amount of sisters, with x standing for the amount of brothers, is x+1. As each brother has twice as many sisters as brothers, the amount of sisters must equal 2(x-1) or 2x-2. To find the number of brother: x+1=2x+1, 1=x-2, 3=x, which means that their are 3 brothers and 4 sisters (x+1= the number of sisters and x=3). This makes sense because a sister would have an equal amount of brothers to sisters, 3 sisters and 3 brothers, if there were 4 sisters and 3 brothers total, and each brother would have 4 sisters and 3 brothers, which is twice the amount of brothers to sisters.

17~21

Audrey Chen

==17.The zero point on a bathroom scale is set incorrectly, but otherwise the scale is accurate. It shows 60 kg when Dan stands on the scale, 50 kg when Sarah stands on the scale, but 105 kg when Dan and Sarah both stand on the scale. Does the scale read too high or too low? Explain. ==

''The scale read too low, since Dan is shown as 60kg and Sarah is 50kg, suppose 60+50=110, 105-110=-5, so that means the scale is smaller than 0 in the beginning''

==18. Alice takes one-third of the pennies from a large jar. Then Bret takes one-third of the remaining pennies from the jar. Finally, Carla takes one-third of the remaining pennies from the jar, leaving 40 pennies in the jar. How many pennies were in the jar at the start? ==

''If the total pennies is "x", Alice take 1/3x, so it has 2/3x left after Alice took it, than Bret take 1/3 out, after Alice took it, which is 2/3x*1/3= 2/9x, so in the beginning they have x, after Alice took it, it has 2/3x left, and Bret took 2/9x, so after Bret took it, it becomes 2/3x-2/9x= 4/9x-2/9x=2/9x left in the jar. Than Carla take 1/3 of the rest, so she took 1/3 of rest which is 2/9x*1/3=3/27x, so Alice took 1/3x, Bret tool 2/9x, Carla took 3/27x, three of them totaly took 1/3x+2/9x+3/27x=18/27x, so there still has x-18/27x= 9/27x= 1/3 left, 1/3x=40pennies, so x=120 pennies, so it was having 120 pennies in the jar.

==19. One morning each member of Angela's family drank an eight-ounce cup of coffee and milk, with the (nonzero) amounts of coffee and milk varying from cup to cup. Angela drank a quarter of the total amount of milk and a sixth of the total amount of coffee. What is the least number of people in the family? ==

''If we let total milk is x, total coffee is y. Than 1/4x+1/6y=8, and because every cup is 8ounce, x+y is multiple by 8. So make it easier, we use 1/4x+1/6y=8 * 12 to both sides. than we will got 3x+2y=96, now we have 3x+2y=96 and x+y is multiple of 8, and the number that multiple by 8 is 8, 16, 24, 32... so 2x+2y= 16, 32, 48, 64, 80, 96, since 3x+2y=96, it can't be more than 96. It will only have 6 possible number, so if you take 3x+2y=96 substracting 2x+2y=16, 32, 48, 64, 80, 96 you can get 6 possible x, which are 80, 64, 48, 32, 16, and 0. Than put the number into 3x+2y=96, if you put 80 in, will get 20, which is bigger than 8, and also 64, 48. If we use 32, it will equal to 8, but that means we have 0 coffee, but coffee can't be 0, so there's only 16 and 0 left. Since Angela had 1/4 of total amount of milk, milk can't be 0. So we got 16ounce than 16*(1/4)=4, so that means she had 8-4=4 's coffee. So 4=1/6 coffee, than the total amount of coffee would be 4*6=24. than x=16 and y=24, 16+24=40 40/8ounce=5, so at least have 5 cups of drinks, so that means at least they have 5 members in Angela's family.''

==20.Of two clocks next to each other, one runs 5 min per hour fast and the other runs 5 min per hour slow. At midnight the clocks show the same time. At what time are they are one hour apart? ==

''Since one clock runs 5 min faster per hour, the other is 5 min slower, after clock runs an hour, two clocks will have 10 min different from each other. 60 min an hour. 60/10=6, so after 6 hours two clocks will having one hour apart, and that would be 6AM.''

==21.Sven placed exactly in the middle among all runners in a race. Dan was slower than Sven, in 10th place, and Lars was in 16th place. How many runners were in the race? ==

''There were 17 runners. Since lars was in 16th place, the runners at least have to be 16, than if Sven is placed exactly in the middle, it means it would have even number of runners. Because Dan is slower and he was at 10 place that tells us Seven has to be before 10th, and if there has 19 runners, Sven and Dan would be at the same place, so it should be 17 runners, than Sven would be at exactly in the middle which at 9th place.''

==22-25==

Roland Will

22. During a vacation, it rained on 13 days, but when it rained in the morning, the afternoon was sunny, and every rainy afternoon was preceded by a sunny morning. There were 11 sunny mornings and 12 sunny afternoons. How long was the vacation?

Answer: 18 days of vacation.

Solution: 13 of the days of vacation were half sunny and half rainy. As there were 23 sunny mornings and afternoons (11 sunny mornings+12 sunny afternoons = 23 sunny mornings and afternoons), 13 of those sunny afternoons or mornings were on half rainy days. This means there are 10 sunny half-days left over, which equal 5 sunny full days. The 5 sunny full days plus the 13 half sunny/rainy days equal 18 total days of vacation.

23. Suppose you overhear the following conversation: Paul: How old are your three children? Paula: The product of their ages is 36 and the sum of their ages is the same as today's date. Paul: That is not enough information. Paula: The oldest child also has red hair. If you were Paul could you determine the ages of Paula's children? Explain.

Answer: If I were Paul this might be possible, but since we don’t know the date that Paula said this, it is not possible for us to find out.

Solution: There are many different combinations of three numbers that can be multiplied and will produce 36. As we do not know the date that Paula said this, the only thing we can be sure of is that the sum of the ages is less than 31 because no month has more than 31 days. Unfortunately, only one set of ages (ages 1 year old, 1 year old and 36 years old) has a sum greater than 31, which leaves many possible combinations open as possible. For today’s date, the 13th, ages of 2, 2, and 9 would produce 36 and have a sum of 13, but, again, it is uncertain. If it were the first of the month, there would be no possible combinations that would produce 36 and sum 1.

24. Two candles of equal length were lit at the same time. One candle took 6 hr to burn out and the other candle took 3 hr to burn out. After how much time was one candle exactly twice as long as the other candle?

Answer: 2 hours.

Solution: The faster burning candle took half the time to burn as the slower burning candle (3 hours/ 6 hours = 1/2), meaning it burned twice as fast. This means that after 2/3 of the total burning time for the faster burning candle it will be 1/3 of its original height and at the slower burning candle will be at 2/3 of its original height and 1/3 is half of 2/3. Since the faster burning candle took 3 hours to burn, 2/3 of its total burning time is 2 hours.

25. Two candles of length L and L + 1 were lit at 6:00 and 4:30, respectively. At 8:30 they had the same length. The longer candle died at 10:30 and the shorter candle died at 10:00. Find L.

Answer: L=2.

Solution: The shorter candle lasted for 4 hours and the longer candle lasted for 6 hours. As 6 hours – 4 hours = 2 hours and 2 hours / 4 hours = 1/2, the longer candle lasted 50% longer and was, therefore, 50% longer in length. This means that the +1 in L+1 on the longer candle was 1/2 of L. 1/2L=1, so L=2*1, L=2.

Course:MATH110/Archive/2010-2011/003/Groups/Group 18

2010-11-12T05:26:43Z

RolandWill: /* 17~21 */

{{Infobox MATH110 Groups
| group number = 18
| member 1 = [[User:ChouJuChen|Audrey Chen]]
| member 2 = [[User:SifatHasan|Sifat Hasan]]
| member 3 = [[User:CaitlinLastiwkaFarquharson|Caitlin Lastiwka-Farquharson]]
| member 4 = [[User:VictoriaWall|Victoria Wall]]
| member 5 = [[User:RolandWill|Roland Will]]
| member 6 =
}}

==Sub-Pages==

Basic Skills Project [http://wiki.ubc.ca/Course:MATH110/003/Groups/Group_18/Basic_Skills_Project]

==Homework due October 20th, 2010==

I created a page for our homework due tomorrow: [http://wiki.ubc.ca/Course:MATH110/003/Groups/Group_18/Homework_October_20th,_2010 http://wiki.ubc.ca/Course:MATH110/003/Groups/Group 18/Homework October 20th, 2010]

-Roland

I've moved the page, it was missing the ''Course:'' part which means it was created directly inside the wiki and not as a subpage of your group page, which is something the wiki admins don't like that much. By the way, you're allowed to use spaces in the name of your pages.

-- [[User:DavidKohler|DavidKohler]] 06:28, 20 October 2010 (UTC)

1-5

Victoria Wall

1.A bus traveled from the terminal to the airport at an average speed of 30 mi/hr and the trip took an hour and 20 min. The bus then traveled from the airport back to the terminal and again averaged 30 mi/hr. However, the return trip required 80 min. Explain.

' 'Lets call the terminal T and the airport A. If the bus travelled from T to A at 30mi/hr and it took them one hour and 20 mins to get from T to A at this speed, and there are 60 minutes in one hour, it took the bus 60min + 20min to get to A which is a total of 80min. The bus took 80 min to get from T to A. To get from A to T at the same speed (30mi/hr) it took the bus 80min. 80min = 80 min. This means going from A to T or vis versa at 30 mi/hr it will take the bus 80min.

2.A lady did not have her driver's license with her when she failed to stop at a stop sign and then went three blocks down a one-way street the wrong way. A policeman saw her, but he did not stop her. Explain.

' 'The lady was walking. It never says she was driving.

3.One of three boxes contains apples, another box contains oranges, and another box contains a mixture of apples and oranges. The boxes are labeled APPLES, ORANGES and APPLES AND ORANGES, but each label is incorrect. Can you select one fruit from only one box and determine the correct labels? Explain.

' 'if you selecet from the box APPLES AND ORANGES then you will be able to see the labels if they are correct or not.

4.I am the brother of the blind fiddler, but brothers I have none. How can this be?

' 'Since it says that he is the brother of the blind fiddler it does not mean that the fiddle is male, since he has no brothers than the fiddler must be a female.

5.Two quarters rest next to each other on a table. One coin is held fixed while the second coin is rolled around the edge of the first coin with no slipping. When the moving coin returns to its original position, how many times has it revolved?

' 'This is because the moving quarters revolves two full revolutions

6-10

Caitlin Lastiwka- Farquharson

6. Three kinds of apples are all mixed up in a basket. How many apples must you draw without (without looking) from the basket to be sure of getting at least two of a kind?

' ' To be sure you are getting at least two of a kind, you must select all of the other types of apples, plus two more. Meaning that only once you have selected all of the other apples can you be sure that you will select two of the kind you desire. It can be written like this: x,a x2, b and x3, c, with x representing the quantity of apples. This can be calculated by x2 + x3 +2. X2 representing one of the types of apples, x3 representing the other type and 2 representing 2 of the kind of apples you are trying to select. This is the only way to be sure you are getting at least two of a kind. ' '

7. Suppose you have 40 blue socks and 40 brown socks in a drawer. How many socks must you take from the drawer (without looking) to be sure of getting (i) a pair of the same colour, and (ii) a pair with different colors.

' 'You must take three socks from the drawer to ensure you have a pair that match. This is because if you only select two, one could be brown and one could be blue. Selecting three, ensures that at least two of them will be the same colour. As for part two, you would need to select 41 socks to ensure you had a pair of different coloured socks because if you select 40 or less you could get all the same colour, but selecting 41 ensures you will have at least one pair of mixed colour. ' '

8. Rueben says "Two days ago I was 20 years old. Later next year I will be 23 years old." Explain how this is possible.

' 'It is possible if your birthday is on the 31st of December and today is the 1st of January. This is because on the 30th of December (two days ago) you we’re 20 years old and now you are 21, later this year you will turn 22 on the 31st of December, and therefore 23 the next year.' '

9. A rope ladder hanging over the side of a boat has rungs one foot apart. Ten rungs are showing. If the tide rises five feet, how many rungs will be showing?

' ' 5 rungs will be showing, because if there are 10 showing now, and they are each a foot apart, then for 5 more rungs to be showing there would need to be an increase in the level of water by 5 feet. ' '

10.Suppose one-half of all people are chocolate eaters and one-half of all people are women. (i) Does it follow that one-fourth of all people are women chocolate eaters? (ii) Does it follow that one-half of all men are chocolate eaters? Explain.

' ' No, it does not follow that one-fourth of all people are women chocolate eaters and it does not follow that half of all men are chocolate eaters because are completely independent scenarios. Meaning that the the amount of women there are does not influence the amount of men that will eat chocolate. For example, If 50% of people are women and 50% of the entire population including men and women eat chocolate (arrived at by using the same logic that if 1/4 of women eat chocolate and 1/4 of men eat chocolate), that entire 50% could be comprised of women, meaning that no men eat chocolate disproving the statement.

11-14

Sifat Hasan

11. A woman, her older brother, her son, and her daughter are chess players. The worst player’s twin, who is one of the four players, and the best player are of opposite sex. The worst player and the best player have the same age. If this is possible, who is the worst player?

The four players (according to age, from oldest to youngest) are: woman's older brother, woman, and the son and the daughter (of the same age). Assuming that the children are of the same age (i.e. twins), the worst player is one of them, since they are the only ones who can have a twin. Assuming that the worst player is the daughter, her brother the son, is of the opposite sex as the woman, therefore the woman is the worst player. However, since the worst and the best player are of the same age, this is not possible, because the twins are of the opposite sex and they are of different genders.

12 A Manhattan fellow had a girlfriend in the Bronx and a girlfriend in Brooklyn. He decided which girlfriend to visit by arriving randomly at the train station and taking the first of the Bronx or Brooklyn trains that arrived. The trains to Brooklyn and the Bronx each arrived regularly every 10 minutes. Not long after he began his scheme the man's Bronx girlfriend left him because he rarely visited. Give a (logical) explanation

Assuming that the Bronx and the Brooklyn train arrive one after the other every 10 minutes, the only logical explanation would be that the man in Manhattan coincidentally went to the station 10 minutes or less before a train to Brooklyn arrived, most of the time.

13 If a clock takes 5 seconds to strike 5:00 (with 5 equally spaced chimes), how long does it take to strike 10:00 (with 10 equally spaced chimes)?

If it takes 5 seconds to strike 5, there will be 4 little halts in the middle. Therefore it takes 5 chimes 4 (5/4) = 1.25 second halts to finish. For 10 chimes, there are 9 halts so, it takes 9x 1.25 = 11.25 seconds for 10 halts.

14 One day in the maternity ward, the name tags for four girl babies became mixed up. (i) In how many different ways could two of the babies be tagged correctly and two of the babies be tagged incorrectly? (ii) In how many different ways could three of the babies be tagged correctly and one baby be tagged incorrectly?

(i)and (ii) If we take the babies names as A,B,C and D. There are 6 different combinations of the mix up, that two babies' names can be correct and 2 can be wrong. Assuming the name tags for the babies A,B,C and D are in respective order, they are ABDC, ADCB, ACBD, DBCA, CBAD and BACD. All other combinations for example BCAD will have one correct and 3 incorrect, or all four of them correct, because if 3 are correct, the fourth one has to be correct.

15-16

Roland Will

15. Alex says to you, “I'll bet you any amount of money that if I shuffle this deck of cards, there will always be as many red cards in the first half of the deck as there are black cards in the second half of the deck.” Should you accept his bet?

Answer: No, you shouldn't assuming the deck has equal amounts of red and black cards as in a standard 52 card deck.
Solution: In a standard 52 card deck, half of the cards (26) are black and half are red. If you take 26 cards at random from the deck, x of them will be black and y of them will be red, and x+y=26. As there are 26 of each color in the deck, then x+?=26 for the black cards in the deck and ?+y=26 for the red cards in the deck. As x+y=26 in the first randomly selected 26 cards, then the value of black cards in the other half of the deck must equal y, and the value of red cards in the other half of the deck must equal x meaning that "there will always be as many red cards in the first half of the deck as there are black cards in the second half of the deck."

16. Suppose that each daughter in your family has the same number of brothers as she has sisters, and each son in your family has twice as many sisters as he has brothers. How many sons and daughters are in the family?

Answer:3 total, 2 sister and 1 brother
Solution: Since the daughters in the family each have as many brothers as sisters the amount of sisters, with x standing for the amount of brothers, is x+1. As each brother has twice as many sisters as brothers, the amount of sisters must equal 2(x-1) or 2x-2. To find the number of brother: x+1=2x+1, 1=x-2, 3=x, which means that their are 3 brothers and 4 sisters (x+1= the number of sisters and x=3). This makes sense because a sister would have an equal amount of brothers to sisters, 3 sisters and 3 brothers, if there were 4 sisters and 3 brothers total, and each brother would have 4 sisters and 3 brothers, which is twice the amount of brothers to sisters.

17~21

==Audrey Chen==

==17.The zero point on a bathroom scale is set incorrectly, but otherwise the scale is accurate. It shows 60 kg when Dan stands on the scale, 50 kg when Sarah stands on the scale, but 105 kg when Dan and Sarah both stand on the scale. Does the scale read too high or too low? Explain. ==

''The scale read too low, since Dan is shown as 60kg and Sarah is 50kg, suppose 60+50=110, 105-110=-5, so that means the scale is smaller than 0 in the beginning''

==18. Alice takes one-third of the pennies from a large jar. Then Bret takes one-third of the remaining pennies from the jar. Finally, Carla takes one-third of the remaining pennies from the jar, leaving 40 pennies in the jar. How many pennies were in the jar at the start? ==

''If the total pennies is "x", Alice take 1/3x, so it has 2/3x left after Alice took it, than Bret take 1/3 out, after Alice took it, which is 2/3x*1/3= 2/9x, so in the beginning they have x, after Alice took it, it has 2/3x left, and Bret took 2/9x, so after Bret took it, it becomes 2/3x-2/9x= 4/9x-2/9x=2/9x left in the jar. Than Carla take 1/3 of the rest, so she took 1/3 of rest which is 2/9x*1/3=3/27x, so Alice took 1/3x, Bret tool 2/9x, Carla took 3/27x, three of them totaly took 1/3x+2/9x+3/27x=18/27x, so there still has x-18/27x= 9/27x= 1/3 left, 1/3x=40pennies, so x=120 pennies, so it was having 120 pennies in the jar.

==19. One morning each member of Angela's family drank an eight-ounce cup of coffee and milk, with the (nonzero) amounts of coffee and milk varying from cup to cup. Angela drank a quarter of the total amount of milk and a sixth of the total amount of coffee. What is the least number of people in the family? ==

''If we let total milk is x, total coffee is y. Than 1/4x+1/6y=8, and because every cup is 8ounce, x+y is multiple by 8. So make it easier, we use 1/4x+1/6y=8 * 12 to both sides. than we will got 3x+2y=96, now we have 3x+2y=96 and x+y is multiple of 8, and the number that multiple by 8 is 8, 16, 24, 32... so 2x+2y= 16, 32, 48, 64, 80, 96, since 3x+2y=96, it can't be more than 96. It will only have 6 possible number, so if you take 3x+2y=96 substracting 2x+2y=16, 32, 48, 64, 80, 96 you can get 6 possible x, which are 80, 64, 48, 32, 16, and 0. Than put the number into 3x+2y=96, if you put 80 in, will get 20, which is bigger than 8, and also 64, 48. If we use 32, it will equal to 8, but that means we have 0 coffee, but coffee can't be 0, so there's only 16 and 0 left. Since Angela had 1/4 of total amount of milk, milk can't be 0. So we got 16ounce than 16*(1/4)=4, so that means she had 8-4=4 's coffee. So 4=1/6 coffee, than the total amount of coffee would be 4*6=24. than x=16 and y=24, 16+24=40 40/8ounce=5, so at least have 5 cups of drinks, so that means at least they have 5 members in Angela's family.''

==20.Of two clocks next to each other, one runs 5 min per hour fast and the other runs 5 min per hour slow. At midnight the clocks show the same time. At what time are they are one hour apart? ==

''Since one clock runs 5 min faster per hour, the other is 5 min slower, after clock runs an hour, two clocks will have 10 min different from each other. 60 min an hour. 60/10=6, so after 6 hours two clocks will having one hour apart, and that would be 6AM.''

==21.Sven placed exactly in the middle among all runners in a race. Dan was slower than Sven, in 10th place, and Lars was in 16th place. How many runners were in the race? ==

''There were 17 runners. Since lars was in 16th place, the runners at least have to be 16, than if Sven is placed exactly in the middle, it means it would have even number of runners. Because Dan is slower and he was at 10 place that tells us Seven has to be before 10th, and if there has 19 runners, Sven and Dan would be at the same place, so it should be 17 runners, than Sven would be at exactly in the middle which at 9th place.''

==22-25==

Roland Will

22. During a vacation, it rained on 13 days, but when it rained in the morning, the afternoon was sunny, and every rainy afternoon was preceded by a sunny morning. There were 11 sunny mornings and 12 sunny afternoons. How long was the vacation?

Answer: 18 days of vacation.

Solution: 13 of the days of vacation were half sunny and half rainy. As there were 23 sunny mornings and afternoons (11 sunny mornings+12 sunny afternoons = 23 sunny mornings and afternoons), 13 of those sunny afternoons or mornings were on half rainy days. This means there are 10 sunny half-days left over, which equal 5 sunny full days. The 5 sunny full days plus the 13 half sunny/rainy days equal 18 total days of vacation.

23. Suppose you overhear the following conversation: Paul: How old are your three children? Paula: The product of their ages is 36 and the sum of their ages is the same as today's date. Paul: That is not enough information. Paula: The oldest child also has red hair. If you were Paul could you determine the ages of Paula's children? Explain.

Answer: If I were Paul this might be possible, but since we don’t know the date that Paula said this, it is not possible for us to find out.

Solution: There are many different combinations of three numbers that can be multiplied and will produce 36. As we do not know the date that Paula said this, the only thing we can be sure of is that the sum of the ages is less than 31 because no month has more than 31 days. Unfortunately, only one set of ages (ages 1 year old, 1 year old and 36 years old) has a sum greater than 31, which leaves many possible combinations open as possible. For today’s date, the 13th, ages of 2, 2, and 9 would produce 36 and have a sum of 13, but, again, it is uncertain. If it were the first of the month, there would be no possible combinations that would produce 36 and sum 1.

24. Two candles of equal length were lit at the same time. One candle took 6 hr to burn out and the other candle took 3 hr to burn out. After how much time was one candle exactly twice as long as the other candle?

Answer: 2 hours.

Solution: The faster burning candle took half the time to burn as the slower burning candle (3 hours/ 6 hours = 1/2), meaning it burned twice as fast. This means that after 2/3 of the total burning time for the faster burning candle it will be 1/3 of its original height and at the slower burning candle will be at 2/3 of its original height and 1/3 is half of 2/3. Since the faster burning candle took 3 hours to burn, 2/3 of its total burning time is 2 hours.

25. Two candles of length L and L + 1 were lit at 6:00 and 4:30, respectively. At 8:30 they had the same length. The longer candle died at 10:30 and the shorter candle died at 10:00. Find L.

Answer: L=2.

Solution: The shorter candle lasted for 4 hours and the longer candle lasted for 6 hours. As 6 hours – 4 hours = 2 hours and 2 hours / 4 hours = 1/2, the longer candle lasted 50% longer and was, therefore, 50% longer in length. This means that the +1 in L+1 on the longer candle was 1/2 of L. 1/2L=1, so L=2*1, L=2.

Course:MATH110/Archive/2010-2011/003/Groups/Group 18

2010-11-12T05:26:31Z

RolandWill: /* 16. Suppose that each daughter in your family has the same number of brothers as she has sisters, and each son in your family has twice as many sisters as he has brothers. How many sons and daughters are in the family? */

{{Infobox MATH110 Groups
| group number = 18
| member 1 = [[User:ChouJuChen|Audrey Chen]]
| member 2 = [[User:SifatHasan|Sifat Hasan]]
| member 3 = [[User:CaitlinLastiwkaFarquharson|Caitlin Lastiwka-Farquharson]]
| member 4 = [[User:VictoriaWall|Victoria Wall]]
| member 5 = [[User:RolandWill|Roland Will]]
| member 6 =
}}

==Sub-Pages==

Basic Skills Project [http://wiki.ubc.ca/Course:MATH110/003/Groups/Group_18/Basic_Skills_Project]

==Homework due October 20th, 2010==

I created a page for our homework due tomorrow: [http://wiki.ubc.ca/Course:MATH110/003/Groups/Group_18/Homework_October_20th,_2010 http://wiki.ubc.ca/Course:MATH110/003/Groups/Group 18/Homework October 20th, 2010]

-Roland

I've moved the page, it was missing the ''Course:'' part which means it was created directly inside the wiki and not as a subpage of your group page, which is something the wiki admins don't like that much. By the way, you're allowed to use spaces in the name of your pages.

-- [[User:DavidKohler|DavidKohler]] 06:28, 20 October 2010 (UTC)

1-5

Victoria Wall

1.A bus traveled from the terminal to the airport at an average speed of 30 mi/hr and the trip took an hour and 20 min. The bus then traveled from the airport back to the terminal and again averaged 30 mi/hr. However, the return trip required 80 min. Explain.

' 'Lets call the terminal T and the airport A. If the bus travelled from T to A at 30mi/hr and it took them one hour and 20 mins to get from T to A at this speed, and there are 60 minutes in one hour, it took the bus 60min + 20min to get to A which is a total of 80min. The bus took 80 min to get from T to A. To get from A to T at the same speed (30mi/hr) it took the bus 80min. 80min = 80 min. This means going from A to T or vis versa at 30 mi/hr it will take the bus 80min.

2.A lady did not have her driver's license with her when she failed to stop at a stop sign and then went three blocks down a one-way street the wrong way. A policeman saw her, but he did not stop her. Explain.

' 'The lady was walking. It never says she was driving.

3.One of three boxes contains apples, another box contains oranges, and another box contains a mixture of apples and oranges. The boxes are labeled APPLES, ORANGES and APPLES AND ORANGES, but each label is incorrect. Can you select one fruit from only one box and determine the correct labels? Explain.

' 'if you selecet from the box APPLES AND ORANGES then you will be able to see the labels if they are correct or not.

4.I am the brother of the blind fiddler, but brothers I have none. How can this be?

' 'Since it says that he is the brother of the blind fiddler it does not mean that the fiddle is male, since he has no brothers than the fiddler must be a female.

5.Two quarters rest next to each other on a table. One coin is held fixed while the second coin is rolled around the edge of the first coin with no slipping. When the moving coin returns to its original position, how many times has it revolved?

' 'This is because the moving quarters revolves two full revolutions

6-10

Caitlin Lastiwka- Farquharson

6. Three kinds of apples are all mixed up in a basket. How many apples must you draw without (without looking) from the basket to be sure of getting at least two of a kind?

' ' To be sure you are getting at least two of a kind, you must select all of the other types of apples, plus two more. Meaning that only once you have selected all of the other apples can you be sure that you will select two of the kind you desire. It can be written like this: x,a x2, b and x3, c, with x representing the quantity of apples. This can be calculated by x2 + x3 +2. X2 representing one of the types of apples, x3 representing the other type and 2 representing 2 of the kind of apples you are trying to select. This is the only way to be sure you are getting at least two of a kind. ' '

7. Suppose you have 40 blue socks and 40 brown socks in a drawer. How many socks must you take from the drawer (without looking) to be sure of getting (i) a pair of the same colour, and (ii) a pair with different colors.

' 'You must take three socks from the drawer to ensure you have a pair that match. This is because if you only select two, one could be brown and one could be blue. Selecting three, ensures that at least two of them will be the same colour. As for part two, you would need to select 41 socks to ensure you had a pair of different coloured socks because if you select 40 or less you could get all the same colour, but selecting 41 ensures you will have at least one pair of mixed colour. ' '

8. Rueben says "Two days ago I was 20 years old. Later next year I will be 23 years old." Explain how this is possible.

' 'It is possible if your birthday is on the 31st of December and today is the 1st of January. This is because on the 30th of December (two days ago) you we’re 20 years old and now you are 21, later this year you will turn 22 on the 31st of December, and therefore 23 the next year.' '

9. A rope ladder hanging over the side of a boat has rungs one foot apart. Ten rungs are showing. If the tide rises five feet, how many rungs will be showing?

' ' 5 rungs will be showing, because if there are 10 showing now, and they are each a foot apart, then for 5 more rungs to be showing there would need to be an increase in the level of water by 5 feet. ' '

10.Suppose one-half of all people are chocolate eaters and one-half of all people are women. (i) Does it follow that one-fourth of all people are women chocolate eaters? (ii) Does it follow that one-half of all men are chocolate eaters? Explain.

' ' No, it does not follow that one-fourth of all people are women chocolate eaters and it does not follow that half of all men are chocolate eaters because are completely independent scenarios. Meaning that the the amount of women there are does not influence the amount of men that will eat chocolate. For example, If 50% of people are women and 50% of the entire population including men and women eat chocolate (arrived at by using the same logic that if 1/4 of women eat chocolate and 1/4 of men eat chocolate), that entire 50% could be comprised of women, meaning that no men eat chocolate disproving the statement.

11-14

Sifat Hasan

11. A woman, her older brother, her son, and her daughter are chess players. The worst player’s twin, who is one of the four players, and the best player are of opposite sex. The worst player and the best player have the same age. If this is possible, who is the worst player?

The four players (according to age, from oldest to youngest) are: woman's older brother, woman, and the son and the daughter (of the same age). Assuming that the children are of the same age (i.e. twins), the worst player is one of them, since they are the only ones who can have a twin. Assuming that the worst player is the daughter, her brother the son, is of the opposite sex as the woman, therefore the woman is the worst player. However, since the worst and the best player are of the same age, this is not possible, because the twins are of the opposite sex and they are of different genders.

12 A Manhattan fellow had a girlfriend in the Bronx and a girlfriend in Brooklyn. He decided which girlfriend to visit by arriving randomly at the train station and taking the first of the Bronx or Brooklyn trains that arrived. The trains to Brooklyn and the Bronx each arrived regularly every 10 minutes. Not long after he began his scheme the man's Bronx girlfriend left him because he rarely visited. Give a (logical) explanation

Assuming that the Bronx and the Brooklyn train arrive one after the other every 10 minutes, the only logical explanation would be that the man in Manhattan coincidentally went to the station 10 minutes or less before a train to Brooklyn arrived, most of the time.

13 If a clock takes 5 seconds to strike 5:00 (with 5 equally spaced chimes), how long does it take to strike 10:00 (with 10 equally spaced chimes)?

If it takes 5 seconds to strike 5, there will be 4 little halts in the middle. Therefore it takes 5 chimes 4 (5/4) = 1.25 second halts to finish. For 10 chimes, there are 9 halts so, it takes 9x 1.25 = 11.25 seconds for 10 halts.

14 One day in the maternity ward, the name tags for four girl babies became mixed up. (i) In how many different ways could two of the babies be tagged correctly and two of the babies be tagged incorrectly? (ii) In how many different ways could three of the babies be tagged correctly and one baby be tagged incorrectly?

(i)and (ii) If we take the babies names as A,B,C and D. There are 6 different combinations of the mix up, that two babies' names can be correct and 2 can be wrong. Assuming the name tags for the babies A,B,C and D are in respective order, they are ABDC, ADCB, ACBD, DBCA, CBAD and BACD. All other combinations for example BCAD will have one correct and 3 incorrect, or all four of them correct, because if 3 are correct, the fourth one has to be correct.

15-16

Roland Will

15. Alex says to you, “I'll bet you any amount of money that if I shuffle this deck of cards, there will always be as many red cards in the first half of the deck as there are black cards in the second half of the deck.” Should you accept his bet?

Answer: No, you shouldn't assuming the deck has equal amounts of red and black cards as in a standard 52 card deck.
Solution: In a standard 52 card deck, half of the cards (26) are black and half are red. If you take 26 cards at random from the deck, x of them will be black and y of them will be red, and x+y=26. As there are 26 of each color in the deck, then x+?=26 for the black cards in the deck and ?+y=26 for the red cards in the deck. As x+y=26 in the first randomly selected 26 cards, then the value of black cards in the other half of the deck must equal y, and the value of red cards in the other half of the deck must equal x meaning that "there will always be as many red cards in the first half of the deck as there are black cards in the second half of the deck."

16. Suppose that each daughter in your family has the same number of brothers as she has sisters, and each son in your family has twice as many sisters as he has brothers. How many sons and daughters are in the family?

Answer:3 total, 2 sister and 1 brother
Solution: Since the daughters in the family each have as many brothers as sisters the amount of sisters, with x standing for the amount of brothers, is x+1. As each brother has twice as many sisters as brothers, the amount of sisters must equal 2(x-1) or 2x-2. To find the number of brother: x+1=2x+1, 1=x-2, 3=x, which means that their are 3 brothers and 4 sisters (x+1= the number of sisters and x=3). This makes sense because a sister would have an equal amount of brothers to sisters, 3 sisters and 3 brothers, if there were 4 sisters and 3 brothers total, and each brother would have 4 sisters and 3 brothers, which is twice the amount of brothers to sisters.

==17~21==
==Audrey Chen==

==17.The zero point on a bathroom scale is set incorrectly, but otherwise the scale is accurate. It shows 60 kg when Dan stands on the scale, 50 kg when Sarah stands on the scale, but 105 kg when Dan and Sarah both stand on the scale. Does the scale read too high or too low? Explain. ==

''The scale read too low, since Dan is shown as 60kg and Sarah is 50kg, suppose 60+50=110, 105-110=-5, so that means the scale is smaller than 0 in the beginning''

==18. Alice takes one-third of the pennies from a large jar. Then Bret takes one-third of the remaining pennies from the jar. Finally, Carla takes one-third of the remaining pennies from the jar, leaving 40 pennies in the jar. How many pennies were in the jar at the start? ==

''If the total pennies is "x", Alice take 1/3x, so it has 2/3x left after Alice took it, than Bret take 1/3 out, after Alice took it, which is 2/3x*1/3= 2/9x, so in the beginning they have x, after Alice took it, it has 2/3x left, and Bret took 2/9x, so after Bret took it, it becomes 2/3x-2/9x= 4/9x-2/9x=2/9x left in the jar. Than Carla take 1/3 of the rest, so she took 1/3 of rest which is 2/9x*1/3=3/27x, so Alice took 1/3x, Bret tool 2/9x, Carla took 3/27x, three of them totaly took 1/3x+2/9x+3/27x=18/27x, so there still has x-18/27x= 9/27x= 1/3 left, 1/3x=40pennies, so x=120 pennies, so it was having 120 pennies in the jar.

==19. One morning each member of Angela's family drank an eight-ounce cup of coffee and milk, with the (nonzero) amounts of coffee and milk varying from cup to cup. Angela drank a quarter of the total amount of milk and a sixth of the total amount of coffee. What is the least number of people in the family? ==

''If we let total milk is x, total coffee is y. Than 1/4x+1/6y=8, and because every cup is 8ounce, x+y is multiple by 8. So make it easier, we use 1/4x+1/6y=8 * 12 to both sides. than we will got 3x+2y=96, now we have 3x+2y=96 and x+y is multiple of 8, and the number that multiple by 8 is 8, 16, 24, 32... so 2x+2y= 16, 32, 48, 64, 80, 96, since 3x+2y=96, it can't be more than 96. It will only have 6 possible number, so if you take 3x+2y=96 substracting 2x+2y=16, 32, 48, 64, 80, 96 you can get 6 possible x, which are 80, 64, 48, 32, 16, and 0. Than put the number into 3x+2y=96, if you put 80 in, will get 20, which is bigger than 8, and also 64, 48. If we use 32, it will equal to 8, but that means we have 0 coffee, but coffee can't be 0, so there's only 16 and 0 left. Since Angela had 1/4 of total amount of milk, milk can't be 0. So we got 16ounce than 16*(1/4)=4, so that means she had 8-4=4 's coffee. So 4=1/6 coffee, than the total amount of coffee would be 4*6=24. than x=16 and y=24, 16+24=40 40/8ounce=5, so at least have 5 cups of drinks, so that means at least they have 5 members in Angela's family.''

==20.Of two clocks next to each other, one runs 5 min per hour fast and the other runs 5 min per hour slow. At midnight the clocks show the same time. At what time are they are one hour apart? ==

''Since one clock runs 5 min faster per hour, the other is 5 min slower, after clock runs an hour, two clocks will have 10 min different from each other. 60 min an hour. 60/10=6, so after 6 hours two clocks will having one hour apart, and that would be 6AM.''

==21.Sven placed exactly in the middle among all runners in a race. Dan was slower than Sven, in 10th place, and Lars was in 16th place. How many runners were in the race? ==

''There were 17 runners. Since lars was in 16th place, the runners at least have to be 16, than if Sven is placed exactly in the middle, it means it would have even number of runners. Because Dan is slower and he was at 10 place that tells us Seven has to be before 10th, and if there has 19 runners, Sven and Dan would be at the same place, so it should be 17 runners, than Sven would be at exactly in the middle which at 9th place.''

==22-25==

Roland Will

22. During a vacation, it rained on 13 days, but when it rained in the morning, the afternoon was sunny, and every rainy afternoon was preceded by a sunny morning. There were 11 sunny mornings and 12 sunny afternoons. How long was the vacation?

Answer: 18 days of vacation.

Solution: 13 of the days of vacation were half sunny and half rainy. As there were 23 sunny mornings and afternoons (11 sunny mornings+12 sunny afternoons = 23 sunny mornings and afternoons), 13 of those sunny afternoons or mornings were on half rainy days. This means there are 10 sunny half-days left over, which equal 5 sunny full days. The 5 sunny full days plus the 13 half sunny/rainy days equal 18 total days of vacation.

23. Suppose you overhear the following conversation: Paul: How old are your three children? Paula: The product of their ages is 36 and the sum of their ages is the same as today's date. Paul: That is not enough information. Paula: The oldest child also has red hair. If you were Paul could you determine the ages of Paula's children? Explain.

Answer: If I were Paul this might be possible, but since we don’t know the date that Paula said this, it is not possible for us to find out.

Solution: There are many different combinations of three numbers that can be multiplied and will produce 36. As we do not know the date that Paula said this, the only thing we can be sure of is that the sum of the ages is less than 31 because no month has more than 31 days. Unfortunately, only one set of ages (ages 1 year old, 1 year old and 36 years old) has a sum greater than 31, which leaves many possible combinations open as possible. For today’s date, the 13th, ages of 2, 2, and 9 would produce 36 and have a sum of 13, but, again, it is uncertain. If it were the first of the month, there would be no possible combinations that would produce 36 and sum 1.

24. Two candles of equal length were lit at the same time. One candle took 6 hr to burn out and the other candle took 3 hr to burn out. After how much time was one candle exactly twice as long as the other candle?

Answer: 2 hours.

Solution: The faster burning candle took half the time to burn as the slower burning candle (3 hours/ 6 hours = 1/2), meaning it burned twice as fast. This means that after 2/3 of the total burning time for the faster burning candle it will be 1/3 of its original height and at the slower burning candle will be at 2/3 of its original height and 1/3 is half of 2/3. Since the faster burning candle took 3 hours to burn, 2/3 of its total burning time is 2 hours.

25. Two candles of length L and L + 1 were lit at 6:00 and 4:30, respectively. At 8:30 they had the same length. The longer candle died at 10:30 and the shorter candle died at 10:00. Find L.

Answer: L=2.

Solution: The shorter candle lasted for 4 hours and the longer candle lasted for 6 hours. As 6 hours – 4 hours = 2 hours and 2 hours / 4 hours = 1/2, the longer candle lasted 50% longer and was, therefore, 50% longer in length. This means that the +1 in L+1 on the longer candle was 1/2 of L. 1/2L=1, so L=2*1, L=2.

Course:MATH110/Archive/2010-2011/003/Groups/Group 18

2010-11-12T05:26:20Z

RolandWill: /* 15. Alex says to you, “I'll bet you any amount of money that if I shuffle this deck of cards, there will always be as many red cards in the first half of the deck as there are black cards in the second half of the deck.” Should you accept his

{{Infobox MATH110 Groups
| group number = 18
| member 1 = [[User:ChouJuChen|Audrey Chen]]
| member 2 = [[User:SifatHasan|Sifat Hasan]]
| member 3 = [[User:CaitlinLastiwkaFarquharson|Caitlin Lastiwka-Farquharson]]
| member 4 = [[User:VictoriaWall|Victoria Wall]]
| member 5 = [[User:RolandWill|Roland Will]]
| member 6 =
}}

==Sub-Pages==

Basic Skills Project [http://wiki.ubc.ca/Course:MATH110/003/Groups/Group_18/Basic_Skills_Project]

==Homework due October 20th, 2010==

I created a page for our homework due tomorrow: [http://wiki.ubc.ca/Course:MATH110/003/Groups/Group_18/Homework_October_20th,_2010 http://wiki.ubc.ca/Course:MATH110/003/Groups/Group 18/Homework October 20th, 2010]

-Roland

I've moved the page, it was missing the ''Course:'' part which means it was created directly inside the wiki and not as a subpage of your group page, which is something the wiki admins don't like that much. By the way, you're allowed to use spaces in the name of your pages.

-- [[User:DavidKohler|DavidKohler]] 06:28, 20 October 2010 (UTC)

1-5

Victoria Wall

1.A bus traveled from the terminal to the airport at an average speed of 30 mi/hr and the trip took an hour and 20 min. The bus then traveled from the airport back to the terminal and again averaged 30 mi/hr. However, the return trip required 80 min. Explain.

' 'Lets call the terminal T and the airport A. If the bus travelled from T to A at 30mi/hr and it took them one hour and 20 mins to get from T to A at this speed, and there are 60 minutes in one hour, it took the bus 60min + 20min to get to A which is a total of 80min. The bus took 80 min to get from T to A. To get from A to T at the same speed (30mi/hr) it took the bus 80min. 80min = 80 min. This means going from A to T or vis versa at 30 mi/hr it will take the bus 80min.

2.A lady did not have her driver's license with her when she failed to stop at a stop sign and then went three blocks down a one-way street the wrong way. A policeman saw her, but he did not stop her. Explain.

' 'The lady was walking. It never says she was driving.

3.One of three boxes contains apples, another box contains oranges, and another box contains a mixture of apples and oranges. The boxes are labeled APPLES, ORANGES and APPLES AND ORANGES, but each label is incorrect. Can you select one fruit from only one box and determine the correct labels? Explain.

' 'if you selecet from the box APPLES AND ORANGES then you will be able to see the labels if they are correct or not.

4.I am the brother of the blind fiddler, but brothers I have none. How can this be?

' 'Since it says that he is the brother of the blind fiddler it does not mean that the fiddle is male, since he has no brothers than the fiddler must be a female.

5.Two quarters rest next to each other on a table. One coin is held fixed while the second coin is rolled around the edge of the first coin with no slipping. When the moving coin returns to its original position, how many times has it revolved?

' 'This is because the moving quarters revolves two full revolutions

6-10

Caitlin Lastiwka- Farquharson

6. Three kinds of apples are all mixed up in a basket. How many apples must you draw without (without looking) from the basket to be sure of getting at least two of a kind?

' ' To be sure you are getting at least two of a kind, you must select all of the other types of apples, plus two more. Meaning that only once you have selected all of the other apples can you be sure that you will select two of the kind you desire. It can be written like this: x,a x2, b and x3, c, with x representing the quantity of apples. This can be calculated by x2 + x3 +2. X2 representing one of the types of apples, x3 representing the other type and 2 representing 2 of the kind of apples you are trying to select. This is the only way to be sure you are getting at least two of a kind. ' '

7. Suppose you have 40 blue socks and 40 brown socks in a drawer. How many socks must you take from the drawer (without looking) to be sure of getting (i) a pair of the same colour, and (ii) a pair with different colors.

' 'You must take three socks from the drawer to ensure you have a pair that match. This is because if you only select two, one could be brown and one could be blue. Selecting three, ensures that at least two of them will be the same colour. As for part two, you would need to select 41 socks to ensure you had a pair of different coloured socks because if you select 40 or less you could get all the same colour, but selecting 41 ensures you will have at least one pair of mixed colour. ' '

8. Rueben says "Two days ago I was 20 years old. Later next year I will be 23 years old." Explain how this is possible.

' 'It is possible if your birthday is on the 31st of December and today is the 1st of January. This is because on the 30th of December (two days ago) you we’re 20 years old and now you are 21, later this year you will turn 22 on the 31st of December, and therefore 23 the next year.' '

9. A rope ladder hanging over the side of a boat has rungs one foot apart. Ten rungs are showing. If the tide rises five feet, how many rungs will be showing?

' ' 5 rungs will be showing, because if there are 10 showing now, and they are each a foot apart, then for 5 more rungs to be showing there would need to be an increase in the level of water by 5 feet. ' '

10.Suppose one-half of all people are chocolate eaters and one-half of all people are women. (i) Does it follow that one-fourth of all people are women chocolate eaters? (ii) Does it follow that one-half of all men are chocolate eaters? Explain.

' ' No, it does not follow that one-fourth of all people are women chocolate eaters and it does not follow that half of all men are chocolate eaters because are completely independent scenarios. Meaning that the the amount of women there are does not influence the amount of men that will eat chocolate. For example, If 50% of people are women and 50% of the entire population including men and women eat chocolate (arrived at by using the same logic that if 1/4 of women eat chocolate and 1/4 of men eat chocolate), that entire 50% could be comprised of women, meaning that no men eat chocolate disproving the statement.

11-14

Sifat Hasan

11. A woman, her older brother, her son, and her daughter are chess players. The worst player’s twin, who is one of the four players, and the best player are of opposite sex. The worst player and the best player have the same age. If this is possible, who is the worst player?

The four players (according to age, from oldest to youngest) are: woman's older brother, woman, and the son and the daughter (of the same age). Assuming that the children are of the same age (i.e. twins), the worst player is one of them, since they are the only ones who can have a twin. Assuming that the worst player is the daughter, her brother the son, is of the opposite sex as the woman, therefore the woman is the worst player. However, since the worst and the best player are of the same age, this is not possible, because the twins are of the opposite sex and they are of different genders.

12 A Manhattan fellow had a girlfriend in the Bronx and a girlfriend in Brooklyn. He decided which girlfriend to visit by arriving randomly at the train station and taking the first of the Bronx or Brooklyn trains that arrived. The trains to Brooklyn and the Bronx each arrived regularly every 10 minutes. Not long after he began his scheme the man's Bronx girlfriend left him because he rarely visited. Give a (logical) explanation

Assuming that the Bronx and the Brooklyn train arrive one after the other every 10 minutes, the only logical explanation would be that the man in Manhattan coincidentally went to the station 10 minutes or less before a train to Brooklyn arrived, most of the time.

13 If a clock takes 5 seconds to strike 5:00 (with 5 equally spaced chimes), how long does it take to strike 10:00 (with 10 equally spaced chimes)?

If it takes 5 seconds to strike 5, there will be 4 little halts in the middle. Therefore it takes 5 chimes 4 (5/4) = 1.25 second halts to finish. For 10 chimes, there are 9 halts so, it takes 9x 1.25 = 11.25 seconds for 10 halts.

14 One day in the maternity ward, the name tags for four girl babies became mixed up. (i) In how many different ways could two of the babies be tagged correctly and two of the babies be tagged incorrectly? (ii) In how many different ways could three of the babies be tagged correctly and one baby be tagged incorrectly?

(i)and (ii) If we take the babies names as A,B,C and D. There are 6 different combinations of the mix up, that two babies' names can be correct and 2 can be wrong. Assuming the name tags for the babies A,B,C and D are in respective order, they are ABDC, ADCB, ACBD, DBCA, CBAD and BACD. All other combinations for example BCAD will have one correct and 3 incorrect, or all four of them correct, because if 3 are correct, the fourth one has to be correct.

15-16

Roland Will

15. Alex says to you, “I'll bet you any amount of money that if I shuffle this deck of cards, there will always be as many red cards in the first half of the deck as there are black cards in the second half of the deck.” Should you accept his bet?

Answer: No, you shouldn't assuming the deck has equal amounts of red and black cards as in a standard 52 card deck.
Solution: In a standard 52 card deck, half of the cards (26) are black and half are red. If you take 26 cards at random from the deck, x of them will be black and y of them will be red, and x+y=26. As there are 26 of each color in the deck, then x+?=26 for the black cards in the deck and ?+y=26 for the red cards in the deck. As x+y=26 in the first randomly selected 26 cards, then the value of black cards in the other half of the deck must equal y, and the value of red cards in the other half of the deck must equal x meaning that "there will always be as many red cards in the first half of the deck as there are black cards in the second half of the deck."

==16. Suppose that each daughter in your family has the same number of brothers as she has sisters, and each son in your family has twice as many sisters as he has brothers. How many sons and daughters are in the family?==

Answer:3 total, 2 sister and 1 brother
Solution: Since the daughters in the family each have as many brothers as sisters the amount of sisters, with x standing for the amount of brothers, is x+1. As each brother has twice as many sisters as brothers, the amount of sisters must equal 2(x-1) or 2x-2. To find the number of brother: x+1=2x+1, 1=x-2, 3=x, which means that their are 3 brothers and 4 sisters (x+1= the number of sisters and x=3). This makes sense because a sister would have an equal amount of brothers to sisters, 3 sisters and 3 brothers, if there were 4 sisters and 3 brothers total, and each brother would have 4 sisters and 3 brothers, which is twice the amount of brothers to sisters.

==17~21==
==Audrey Chen==

==17.The zero point on a bathroom scale is set incorrectly, but otherwise the scale is accurate. It shows 60 kg when Dan stands on the scale, 50 kg when Sarah stands on the scale, but 105 kg when Dan and Sarah both stand on the scale. Does the scale read too high or too low? Explain. ==

''The scale read too low, since Dan is shown as 60kg and Sarah is 50kg, suppose 60+50=110, 105-110=-5, so that means the scale is smaller than 0 in the beginning''

==18. Alice takes one-third of the pennies from a large jar. Then Bret takes one-third of the remaining pennies from the jar. Finally, Carla takes one-third of the remaining pennies from the jar, leaving 40 pennies in the jar. How many pennies were in the jar at the start? ==

''If the total pennies is "x", Alice take 1/3x, so it has 2/3x left after Alice took it, than Bret take 1/3 out, after Alice took it, which is 2/3x*1/3= 2/9x, so in the beginning they have x, after Alice took it, it has 2/3x left, and Bret took 2/9x, so after Bret took it, it becomes 2/3x-2/9x= 4/9x-2/9x=2/9x left in the jar. Than Carla take 1/3 of the rest, so she took 1/3 of rest which is 2/9x*1/3=3/27x, so Alice took 1/3x, Bret tool 2/9x, Carla took 3/27x, three of them totaly took 1/3x+2/9x+3/27x=18/27x, so there still has x-18/27x= 9/27x= 1/3 left, 1/3x=40pennies, so x=120 pennies, so it was having 120 pennies in the jar.

==19. One morning each member of Angela's family drank an eight-ounce cup of coffee and milk, with the (nonzero) amounts of coffee and milk varying from cup to cup. Angela drank a quarter of the total amount of milk and a sixth of the total amount of coffee. What is the least number of people in the family? ==

''If we let total milk is x, total coffee is y. Than 1/4x+1/6y=8, and because every cup is 8ounce, x+y is multiple by 8. So make it easier, we use 1/4x+1/6y=8 * 12 to both sides. than we will got 3x+2y=96, now we have 3x+2y=96 and x+y is multiple of 8, and the number that multiple by 8 is 8, 16, 24, 32... so 2x+2y= 16, 32, 48, 64, 80, 96, since 3x+2y=96, it can't be more than 96. It will only have 6 possible number, so if you take 3x+2y=96 substracting 2x+2y=16, 32, 48, 64, 80, 96 you can get 6 possible x, which are 80, 64, 48, 32, 16, and 0. Than put the number into 3x+2y=96, if you put 80 in, will get 20, which is bigger than 8, and also 64, 48. If we use 32, it will equal to 8, but that means we have 0 coffee, but coffee can't be 0, so there's only 16 and 0 left. Since Angela had 1/4 of total amount of milk, milk can't be 0. So we got 16ounce than 16*(1/4)=4, so that means she had 8-4=4 's coffee. So 4=1/6 coffee, than the total amount of coffee would be 4*6=24. than x=16 and y=24, 16+24=40 40/8ounce=5, so at least have 5 cups of drinks, so that means at least they have 5 members in Angela's family.''

==20.Of two clocks next to each other, one runs 5 min per hour fast and the other runs 5 min per hour slow. At midnight the clocks show the same time. At what time are they are one hour apart? ==

''Since one clock runs 5 min faster per hour, the other is 5 min slower, after clock runs an hour, two clocks will have 10 min different from each other. 60 min an hour. 60/10=6, so after 6 hours two clocks will having one hour apart, and that would be 6AM.''

==21.Sven placed exactly in the middle among all runners in a race. Dan was slower than Sven, in 10th place, and Lars was in 16th place. How many runners were in the race? ==

''There were 17 runners. Since lars was in 16th place, the runners at least have to be 16, than if Sven is placed exactly in the middle, it means it would have even number of runners. Because Dan is slower and he was at 10 place that tells us Seven has to be before 10th, and if there has 19 runners, Sven and Dan would be at the same place, so it should be 17 runners, than Sven would be at exactly in the middle which at 9th place.''

==22-25==

Roland Will

22. During a vacation, it rained on 13 days, but when it rained in the morning, the afternoon was sunny, and every rainy afternoon was preceded by a sunny morning. There were 11 sunny mornings and 12 sunny afternoons. How long was the vacation?

Answer: 18 days of vacation.

Solution: 13 of the days of vacation were half sunny and half rainy. As there were 23 sunny mornings and afternoons (11 sunny mornings+12 sunny afternoons = 23 sunny mornings and afternoons), 13 of those sunny afternoons or mornings were on half rainy days. This means there are 10 sunny half-days left over, which equal 5 sunny full days. The 5 sunny full days plus the 13 half sunny/rainy days equal 18 total days of vacation.

23. Suppose you overhear the following conversation: Paul: How old are your three children? Paula: The product of their ages is 36 and the sum of their ages is the same as today's date. Paul: That is not enough information. Paula: The oldest child also has red hair. If you were Paul could you determine the ages of Paula's children? Explain.

Answer: If I were Paul this might be possible, but since we don’t know the date that Paula said this, it is not possible for us to find out.

Solution: There are many different combinations of three numbers that can be multiplied and will produce 36. As we do not know the date that Paula said this, the only thing we can be sure of is that the sum of the ages is less than 31 because no month has more than 31 days. Unfortunately, only one set of ages (ages 1 year old, 1 year old and 36 years old) has a sum greater than 31, which leaves many possible combinations open as possible. For today’s date, the 13th, ages of 2, 2, and 9 would produce 36 and have a sum of 13, but, again, it is uncertain. If it were the first of the month, there would be no possible combinations that would produce 36 and sum 1.

24. Two candles of equal length were lit at the same time. One candle took 6 hr to burn out and the other candle took 3 hr to burn out. After how much time was one candle exactly twice as long as the other candle?

Answer: 2 hours.

Solution: The faster burning candle took half the time to burn as the slower burning candle (3 hours/ 6 hours = 1/2), meaning it burned twice as fast. This means that after 2/3 of the total burning time for the faster burning candle it will be 1/3 of its original height and at the slower burning candle will be at 2/3 of its original height and 1/3 is half of 2/3. Since the faster burning candle took 3 hours to burn, 2/3 of its total burning time is 2 hours.

25. Two candles of length L and L + 1 were lit at 6:00 and 4:30, respectively. At 8:30 they had the same length. The longer candle died at 10:30 and the shorter candle died at 10:00. Find L.

Answer: L=2.

Solution: The shorter candle lasted for 4 hours and the longer candle lasted for 6 hours. As 6 hours – 4 hours = 2 hours and 2 hours / 4 hours = 1/2, the longer candle lasted 50% longer and was, therefore, 50% longer in length. This means that the +1 in L+1 on the longer candle was 1/2 of L. 1/2L=1, so L=2*1, L=2.

Course:MATH110/Archive/2010-2011/003/Groups/Group 18

2010-11-12T05:26:08Z

RolandWill: /* Roland Will */

{{Infobox MATH110 Groups
| group number = 18
| member 1 = [[User:ChouJuChen|Audrey Chen]]
| member 2 = [[User:SifatHasan|Sifat Hasan]]
| member 3 = [[User:CaitlinLastiwkaFarquharson|Caitlin Lastiwka-Farquharson]]
| member 4 = [[User:VictoriaWall|Victoria Wall]]
| member 5 = [[User:RolandWill|Roland Will]]
| member 6 =
}}

==Sub-Pages==

Basic Skills Project [http://wiki.ubc.ca/Course:MATH110/003/Groups/Group_18/Basic_Skills_Project]

==Homework due October 20th, 2010==

I created a page for our homework due tomorrow: [http://wiki.ubc.ca/Course:MATH110/003/Groups/Group_18/Homework_October_20th,_2010 http://wiki.ubc.ca/Course:MATH110/003/Groups/Group 18/Homework October 20th, 2010]

-Roland

I've moved the page, it was missing the ''Course:'' part which means it was created directly inside the wiki and not as a subpage of your group page, which is something the wiki admins don't like that much. By the way, you're allowed to use spaces in the name of your pages.

-- [[User:DavidKohler|DavidKohler]] 06:28, 20 October 2010 (UTC)

1-5

Victoria Wall

1.A bus traveled from the terminal to the airport at an average speed of 30 mi/hr and the trip took an hour and 20 min. The bus then traveled from the airport back to the terminal and again averaged 30 mi/hr. However, the return trip required 80 min. Explain.

' 'Lets call the terminal T and the airport A. If the bus travelled from T to A at 30mi/hr and it took them one hour and 20 mins to get from T to A at this speed, and there are 60 minutes in one hour, it took the bus 60min + 20min to get to A which is a total of 80min. The bus took 80 min to get from T to A. To get from A to T at the same speed (30mi/hr) it took the bus 80min. 80min = 80 min. This means going from A to T or vis versa at 30 mi/hr it will take the bus 80min.

2.A lady did not have her driver's license with her when she failed to stop at a stop sign and then went three blocks down a one-way street the wrong way. A policeman saw her, but he did not stop her. Explain.

' 'The lady was walking. It never says she was driving.

3.One of three boxes contains apples, another box contains oranges, and another box contains a mixture of apples and oranges. The boxes are labeled APPLES, ORANGES and APPLES AND ORANGES, but each label is incorrect. Can you select one fruit from only one box and determine the correct labels? Explain.

' 'if you selecet from the box APPLES AND ORANGES then you will be able to see the labels if they are correct or not.

4.I am the brother of the blind fiddler, but brothers I have none. How can this be?

' 'Since it says that he is the brother of the blind fiddler it does not mean that the fiddle is male, since he has no brothers than the fiddler must be a female.

5.Two quarters rest next to each other on a table. One coin is held fixed while the second coin is rolled around the edge of the first coin with no slipping. When the moving coin returns to its original position, how many times has it revolved?

' 'This is because the moving quarters revolves two full revolutions

6-10

Caitlin Lastiwka- Farquharson

6. Three kinds of apples are all mixed up in a basket. How many apples must you draw without (without looking) from the basket to be sure of getting at least two of a kind?

' ' To be sure you are getting at least two of a kind, you must select all of the other types of apples, plus two more. Meaning that only once you have selected all of the other apples can you be sure that you will select two of the kind you desire. It can be written like this: x,a x2, b and x3, c, with x representing the quantity of apples. This can be calculated by x2 + x3 +2. X2 representing one of the types of apples, x3 representing the other type and 2 representing 2 of the kind of apples you are trying to select. This is the only way to be sure you are getting at least two of a kind. ' '

7. Suppose you have 40 blue socks and 40 brown socks in a drawer. How many socks must you take from the drawer (without looking) to be sure of getting (i) a pair of the same colour, and (ii) a pair with different colors.

' 'You must take three socks from the drawer to ensure you have a pair that match. This is because if you only select two, one could be brown and one could be blue. Selecting three, ensures that at least two of them will be the same colour. As for part two, you would need to select 41 socks to ensure you had a pair of different coloured socks because if you select 40 or less you could get all the same colour, but selecting 41 ensures you will have at least one pair of mixed colour. ' '

8. Rueben says "Two days ago I was 20 years old. Later next year I will be 23 years old." Explain how this is possible.

' 'It is possible if your birthday is on the 31st of December and today is the 1st of January. This is because on the 30th of December (two days ago) you we’re 20 years old and now you are 21, later this year you will turn 22 on the 31st of December, and therefore 23 the next year.' '

9. A rope ladder hanging over the side of a boat has rungs one foot apart. Ten rungs are showing. If the tide rises five feet, how many rungs will be showing?

' ' 5 rungs will be showing, because if there are 10 showing now, and they are each a foot apart, then for 5 more rungs to be showing there would need to be an increase in the level of water by 5 feet. ' '

10.Suppose one-half of all people are chocolate eaters and one-half of all people are women. (i) Does it follow that one-fourth of all people are women chocolate eaters? (ii) Does it follow that one-half of all men are chocolate eaters? Explain.

' ' No, it does not follow that one-fourth of all people are women chocolate eaters and it does not follow that half of all men are chocolate eaters because are completely independent scenarios. Meaning that the the amount of women there are does not influence the amount of men that will eat chocolate. For example, If 50% of people are women and 50% of the entire population including men and women eat chocolate (arrived at by using the same logic that if 1/4 of women eat chocolate and 1/4 of men eat chocolate), that entire 50% could be comprised of women, meaning that no men eat chocolate disproving the statement.

11-14

Sifat Hasan

11. A woman, her older brother, her son, and her daughter are chess players. The worst player’s twin, who is one of the four players, and the best player are of opposite sex. The worst player and the best player have the same age. If this is possible, who is the worst player?

The four players (according to age, from oldest to youngest) are: woman's older brother, woman, and the son and the daughter (of the same age). Assuming that the children are of the same age (i.e. twins), the worst player is one of them, since they are the only ones who can have a twin. Assuming that the worst player is the daughter, her brother the son, is of the opposite sex as the woman, therefore the woman is the worst player. However, since the worst and the best player are of the same age, this is not possible, because the twins are of the opposite sex and they are of different genders.

12 A Manhattan fellow had a girlfriend in the Bronx and a girlfriend in Brooklyn. He decided which girlfriend to visit by arriving randomly at the train station and taking the first of the Bronx or Brooklyn trains that arrived. The trains to Brooklyn and the Bronx each arrived regularly every 10 minutes. Not long after he began his scheme the man's Bronx girlfriend left him because he rarely visited. Give a (logical) explanation

Assuming that the Bronx and the Brooklyn train arrive one after the other every 10 minutes, the only logical explanation would be that the man in Manhattan coincidentally went to the station 10 minutes or less before a train to Brooklyn arrived, most of the time.

13 If a clock takes 5 seconds to strike 5:00 (with 5 equally spaced chimes), how long does it take to strike 10:00 (with 10 equally spaced chimes)?

If it takes 5 seconds to strike 5, there will be 4 little halts in the middle. Therefore it takes 5 chimes 4 (5/4) = 1.25 second halts to finish. For 10 chimes, there are 9 halts so, it takes 9x 1.25 = 11.25 seconds for 10 halts.

14 One day in the maternity ward, the name tags for four girl babies became mixed up. (i) In how many different ways could two of the babies be tagged correctly and two of the babies be tagged incorrectly? (ii) In how many different ways could three of the babies be tagged correctly and one baby be tagged incorrectly?

(i)and (ii) If we take the babies names as A,B,C and D. There are 6 different combinations of the mix up, that two babies' names can be correct and 2 can be wrong. Assuming the name tags for the babies A,B,C and D are in respective order, they are ABDC, ADCB, ACBD, DBCA, CBAD and BACD. All other combinations for example BCAD will have one correct and 3 incorrect, or all four of them correct, because if 3 are correct, the fourth one has to be correct.

15-16

Roland Will

==15. Alex says to you, “I'll bet you any amount of money that if I shuffle this deck of cards, there will always be as many red cards in the first half of the deck as there are black cards in the second half of the deck.” Should you accept his bet?==

Answer: No, you shouldn't assuming the deck has equal amounts of red and black cards as in a standard 52 card deck.
Solution: In a standard 52 card deck, half of the cards (26) are black and half are red. If you take 26 cards at random from the deck, x of them will be black and y of them will be red, and x+y=26. As there are 26 of each color in the deck, then x+?=26 for the black cards in the deck and ?+y=26 for the red cards in the deck. As x+y=26 in the first randomly selected 26 cards, then the value of black cards in the other half of the deck must equal y, and the value of red cards in the other half of the deck must equal x meaning that "there will always be as many red cards in the first half of the deck as there are black cards in the second half of the deck."

==16. Suppose that each daughter in your family has the same number of brothers as she has sisters, and each son in your family has twice as many sisters as he has brothers. How many sons and daughters are in the family?==

Answer:3 total, 2 sister and 1 brother
Solution: Since the daughters in the family each have as many brothers as sisters the amount of sisters, with x standing for the amount of brothers, is x+1. As each brother has twice as many sisters as brothers, the amount of sisters must equal 2(x-1) or 2x-2. To find the number of brother: x+1=2x+1, 1=x-2, 3=x, which means that their are 3 brothers and 4 sisters (x+1= the number of sisters and x=3). This makes sense because a sister would have an equal amount of brothers to sisters, 3 sisters and 3 brothers, if there were 4 sisters and 3 brothers total, and each brother would have 4 sisters and 3 brothers, which is twice the amount of brothers to sisters.

==17~21==
==Audrey Chen==

==17.The zero point on a bathroom scale is set incorrectly, but otherwise the scale is accurate. It shows 60 kg when Dan stands on the scale, 50 kg when Sarah stands on the scale, but 105 kg when Dan and Sarah both stand on the scale. Does the scale read too high or too low? Explain. ==

''The scale read too low, since Dan is shown as 60kg and Sarah is 50kg, suppose 60+50=110, 105-110=-5, so that means the scale is smaller than 0 in the beginning''

==18. Alice takes one-third of the pennies from a large jar. Then Bret takes one-third of the remaining pennies from the jar. Finally, Carla takes one-third of the remaining pennies from the jar, leaving 40 pennies in the jar. How many pennies were in the jar at the start? ==

''If the total pennies is "x", Alice take 1/3x, so it has 2/3x left after Alice took it, than Bret take 1/3 out, after Alice took it, which is 2/3x*1/3= 2/9x, so in the beginning they have x, after Alice took it, it has 2/3x left, and Bret took 2/9x, so after Bret took it, it becomes 2/3x-2/9x= 4/9x-2/9x=2/9x left in the jar. Than Carla take 1/3 of the rest, so she took 1/3 of rest which is 2/9x*1/3=3/27x, so Alice took 1/3x, Bret tool 2/9x, Carla took 3/27x, three of them totaly took 1/3x+2/9x+3/27x=18/27x, so there still has x-18/27x= 9/27x= 1/3 left, 1/3x=40pennies, so x=120 pennies, so it was having 120 pennies in the jar.

==19. One morning each member of Angela's family drank an eight-ounce cup of coffee and milk, with the (nonzero) amounts of coffee and milk varying from cup to cup. Angela drank a quarter of the total amount of milk and a sixth of the total amount of coffee. What is the least number of people in the family? ==

''If we let total milk is x, total coffee is y. Than 1/4x+1/6y=8, and because every cup is 8ounce, x+y is multiple by 8. So make it easier, we use 1/4x+1/6y=8 * 12 to both sides. than we will got 3x+2y=96, now we have 3x+2y=96 and x+y is multiple of 8, and the number that multiple by 8 is 8, 16, 24, 32... so 2x+2y= 16, 32, 48, 64, 80, 96, since 3x+2y=96, it can't be more than 96. It will only have 6 possible number, so if you take 3x+2y=96 substracting 2x+2y=16, 32, 48, 64, 80, 96 you can get 6 possible x, which are 80, 64, 48, 32, 16, and 0. Than put the number into 3x+2y=96, if you put 80 in, will get 20, which is bigger than 8, and also 64, 48. If we use 32, it will equal to 8, but that means we have 0 coffee, but coffee can't be 0, so there's only 16 and 0 left. Since Angela had 1/4 of total amount of milk, milk can't be 0. So we got 16ounce than 16*(1/4)=4, so that means she had 8-4=4 's coffee. So 4=1/6 coffee, than the total amount of coffee would be 4*6=24. than x=16 and y=24, 16+24=40 40/8ounce=5, so at least have 5 cups of drinks, so that means at least they have 5 members in Angela's family.''

==20.Of two clocks next to each other, one runs 5 min per hour fast and the other runs 5 min per hour slow. At midnight the clocks show the same time. At what time are they are one hour apart? ==

''Since one clock runs 5 min faster per hour, the other is 5 min slower, after clock runs an hour, two clocks will have 10 min different from each other. 60 min an hour. 60/10=6, so after 6 hours two clocks will having one hour apart, and that would be 6AM.''

==21.Sven placed exactly in the middle among all runners in a race. Dan was slower than Sven, in 10th place, and Lars was in 16th place. How many runners were in the race? ==

''There were 17 runners. Since lars was in 16th place, the runners at least have to be 16, than if Sven is placed exactly in the middle, it means it would have even number of runners. Because Dan is slower and he was at 10 place that tells us Seven has to be before 10th, and if there has 19 runners, Sven and Dan would be at the same place, so it should be 17 runners, than Sven would be at exactly in the middle which at 9th place.''

==22-25==

Roland Will

22. During a vacation, it rained on 13 days, but when it rained in the morning, the afternoon was sunny, and every rainy afternoon was preceded by a sunny morning. There were 11 sunny mornings and 12 sunny afternoons. How long was the vacation?

Answer: 18 days of vacation.

Solution: 13 of the days of vacation were half sunny and half rainy. As there were 23 sunny mornings and afternoons (11 sunny mornings+12 sunny afternoons = 23 sunny mornings and afternoons), 13 of those sunny afternoons or mornings were on half rainy days. This means there are 10 sunny half-days left over, which equal 5 sunny full days. The 5 sunny full days plus the 13 half sunny/rainy days equal 18 total days of vacation.

23. Suppose you overhear the following conversation: Paul: How old are your three children? Paula: The product of their ages is 36 and the sum of their ages is the same as today's date. Paul: That is not enough information. Paula: The oldest child also has red hair. If you were Paul could you determine the ages of Paula's children? Explain.

Answer: If I were Paul this might be possible, but since we don’t know the date that Paula said this, it is not possible for us to find out.

Solution: There are many different combinations of three numbers that can be multiplied and will produce 36. As we do not know the date that Paula said this, the only thing we can be sure of is that the sum of the ages is less than 31 because no month has more than 31 days. Unfortunately, only one set of ages (ages 1 year old, 1 year old and 36 years old) has a sum greater than 31, which leaves many possible combinations open as possible. For today’s date, the 13th, ages of 2, 2, and 9 would produce 36 and have a sum of 13, but, again, it is uncertain. If it were the first of the month, there would be no possible combinations that would produce 36 and sum 1.

24. Two candles of equal length were lit at the same time. One candle took 6 hr to burn out and the other candle took 3 hr to burn out. After how much time was one candle exactly twice as long as the other candle?

Answer: 2 hours.

Solution: The faster burning candle took half the time to burn as the slower burning candle (3 hours/ 6 hours = 1/2), meaning it burned twice as fast. This means that after 2/3 of the total burning time for the faster burning candle it will be 1/3 of its original height and at the slower burning candle will be at 2/3 of its original height and 1/3 is half of 2/3. Since the faster burning candle took 3 hours to burn, 2/3 of its total burning time is 2 hours.

25. Two candles of length L and L + 1 were lit at 6:00 and 4:30, respectively. At 8:30 they had the same length. The longer candle died at 10:30 and the shorter candle died at 10:00. Find L.

Answer: L=2.

Solution: The shorter candle lasted for 4 hours and the longer candle lasted for 6 hours. As 6 hours – 4 hours = 2 hours and 2 hours / 4 hours = 1/2, the longer candle lasted 50% longer and was, therefore, 50% longer in length. This means that the +1 in L+1 on the longer candle was 1/2 of L. 1/2L=1, so L=2*1, L=2.

Course:MATH110/Archive/2010-2011/003/Groups/Group 18

2010-11-12T05:25:56Z

RolandWill: /* 15-16 */

{{Infobox MATH110 Groups
| group number = 18
| member 1 = [[User:ChouJuChen|Audrey Chen]]
| member 2 = [[User:SifatHasan|Sifat Hasan]]
| member 3 = [[User:CaitlinLastiwkaFarquharson|Caitlin Lastiwka-Farquharson]]
| member 4 = [[User:VictoriaWall|Victoria Wall]]
| member 5 = [[User:RolandWill|Roland Will]]
| member 6 =
}}

==Sub-Pages==

Basic Skills Project [http://wiki.ubc.ca/Course:MATH110/003/Groups/Group_18/Basic_Skills_Project]

==Homework due October 20th, 2010==

I created a page for our homework due tomorrow: [http://wiki.ubc.ca/Course:MATH110/003/Groups/Group_18/Homework_October_20th,_2010 http://wiki.ubc.ca/Course:MATH110/003/Groups/Group 18/Homework October 20th, 2010]

-Roland

I've moved the page, it was missing the ''Course:'' part which means it was created directly inside the wiki and not as a subpage of your group page, which is something the wiki admins don't like that much. By the way, you're allowed to use spaces in the name of your pages.

-- [[User:DavidKohler|DavidKohler]] 06:28, 20 October 2010 (UTC)

1-5

Victoria Wall

1.A bus traveled from the terminal to the airport at an average speed of 30 mi/hr and the trip took an hour and 20 min. The bus then traveled from the airport back to the terminal and again averaged 30 mi/hr. However, the return trip required 80 min. Explain.

' 'Lets call the terminal T and the airport A. If the bus travelled from T to A at 30mi/hr and it took them one hour and 20 mins to get from T to A at this speed, and there are 60 minutes in one hour, it took the bus 60min + 20min to get to A which is a total of 80min. The bus took 80 min to get from T to A. To get from A to T at the same speed (30mi/hr) it took the bus 80min. 80min = 80 min. This means going from A to T or vis versa at 30 mi/hr it will take the bus 80min.

2.A lady did not have her driver's license with her when she failed to stop at a stop sign and then went three blocks down a one-way street the wrong way. A policeman saw her, but he did not stop her. Explain.

' 'The lady was walking. It never says she was driving.

3.One of three boxes contains apples, another box contains oranges, and another box contains a mixture of apples and oranges. The boxes are labeled APPLES, ORANGES and APPLES AND ORANGES, but each label is incorrect. Can you select one fruit from only one box and determine the correct labels? Explain.

' 'if you selecet from the box APPLES AND ORANGES then you will be able to see the labels if they are correct or not.

4.I am the brother of the blind fiddler, but brothers I have none. How can this be?

' 'Since it says that he is the brother of the blind fiddler it does not mean that the fiddle is male, since he has no brothers than the fiddler must be a female.

5.Two quarters rest next to each other on a table. One coin is held fixed while the second coin is rolled around the edge of the first coin with no slipping. When the moving coin returns to its original position, how many times has it revolved?

' 'This is because the moving quarters revolves two full revolutions

6-10

Caitlin Lastiwka- Farquharson

6. Three kinds of apples are all mixed up in a basket. How many apples must you draw without (without looking) from the basket to be sure of getting at least two of a kind?

' ' To be sure you are getting at least two of a kind, you must select all of the other types of apples, plus two more. Meaning that only once you have selected all of the other apples can you be sure that you will select two of the kind you desire. It can be written like this: x,a x2, b and x3, c, with x representing the quantity of apples. This can be calculated by x2 + x3 +2. X2 representing one of the types of apples, x3 representing the other type and 2 representing 2 of the kind of apples you are trying to select. This is the only way to be sure you are getting at least two of a kind. ' '

7. Suppose you have 40 blue socks and 40 brown socks in a drawer. How many socks must you take from the drawer (without looking) to be sure of getting (i) a pair of the same colour, and (ii) a pair with different colors.

' 'You must take three socks from the drawer to ensure you have a pair that match. This is because if you only select two, one could be brown and one could be blue. Selecting three, ensures that at least two of them will be the same colour. As for part two, you would need to select 41 socks to ensure you had a pair of different coloured socks because if you select 40 or less you could get all the same colour, but selecting 41 ensures you will have at least one pair of mixed colour. ' '

8. Rueben says "Two days ago I was 20 years old. Later next year I will be 23 years old." Explain how this is possible.

' 'It is possible if your birthday is on the 31st of December and today is the 1st of January. This is because on the 30th of December (two days ago) you we’re 20 years old and now you are 21, later this year you will turn 22 on the 31st of December, and therefore 23 the next year.' '

9. A rope ladder hanging over the side of a boat has rungs one foot apart. Ten rungs are showing. If the tide rises five feet, how many rungs will be showing?

' ' 5 rungs will be showing, because if there are 10 showing now, and they are each a foot apart, then for 5 more rungs to be showing there would need to be an increase in the level of water by 5 feet. ' '

10.Suppose one-half of all people are chocolate eaters and one-half of all people are women. (i) Does it follow that one-fourth of all people are women chocolate eaters? (ii) Does it follow that one-half of all men are chocolate eaters? Explain.

' ' No, it does not follow that one-fourth of all people are women chocolate eaters and it does not follow that half of all men are chocolate eaters because are completely independent scenarios. Meaning that the the amount of women there are does not influence the amount of men that will eat chocolate. For example, If 50% of people are women and 50% of the entire population including men and women eat chocolate (arrived at by using the same logic that if 1/4 of women eat chocolate and 1/4 of men eat chocolate), that entire 50% could be comprised of women, meaning that no men eat chocolate disproving the statement.

11-14

Sifat Hasan

11. A woman, her older brother, her son, and her daughter are chess players. The worst player’s twin, who is one of the four players, and the best player are of opposite sex. The worst player and the best player have the same age. If this is possible, who is the worst player?

The four players (according to age, from oldest to youngest) are: woman's older brother, woman, and the son and the daughter (of the same age). Assuming that the children are of the same age (i.e. twins), the worst player is one of them, since they are the only ones who can have a twin. Assuming that the worst player is the daughter, her brother the son, is of the opposite sex as the woman, therefore the woman is the worst player. However, since the worst and the best player are of the same age, this is not possible, because the twins are of the opposite sex and they are of different genders.

12 A Manhattan fellow had a girlfriend in the Bronx and a girlfriend in Brooklyn. He decided which girlfriend to visit by arriving randomly at the train station and taking the first of the Bronx or Brooklyn trains that arrived. The trains to Brooklyn and the Bronx each arrived regularly every 10 minutes. Not long after he began his scheme the man's Bronx girlfriend left him because he rarely visited. Give a (logical) explanation

Assuming that the Bronx and the Brooklyn train arrive one after the other every 10 minutes, the only logical explanation would be that the man in Manhattan coincidentally went to the station 10 minutes or less before a train to Brooklyn arrived, most of the time.

13 If a clock takes 5 seconds to strike 5:00 (with 5 equally spaced chimes), how long does it take to strike 10:00 (with 10 equally spaced chimes)?

If it takes 5 seconds to strike 5, there will be 4 little halts in the middle. Therefore it takes 5 chimes 4 (5/4) = 1.25 second halts to finish. For 10 chimes, there are 9 halts so, it takes 9x 1.25 = 11.25 seconds for 10 halts.

14 One day in the maternity ward, the name tags for four girl babies became mixed up. (i) In how many different ways could two of the babies be tagged correctly and two of the babies be tagged incorrectly? (ii) In how many different ways could three of the babies be tagged correctly and one baby be tagged incorrectly?

(i)and (ii) If we take the babies names as A,B,C and D. There are 6 different combinations of the mix up, that two babies' names can be correct and 2 can be wrong. Assuming the name tags for the babies A,B,C and D are in respective order, they are ABDC, ADCB, ACBD, DBCA, CBAD and BACD. All other combinations for example BCAD will have one correct and 3 incorrect, or all four of them correct, because if 3 are correct, the fourth one has to be correct.

15-16

==Roland Will==

==15. Alex says to you, “I'll bet you any amount of money that if I shuffle this deck of cards, there will always be as many red cards in the first half of the deck as there are black cards in the second half of the deck.” Should you accept his bet?==

Answer: No, you shouldn't assuming the deck has equal amounts of red and black cards as in a standard 52 card deck.
Solution: In a standard 52 card deck, half of the cards (26) are black and half are red. If you take 26 cards at random from the deck, x of them will be black and y of them will be red, and x+y=26. As there are 26 of each color in the deck, then x+?=26 for the black cards in the deck and ?+y=26 for the red cards in the deck. As x+y=26 in the first randomly selected 26 cards, then the value of black cards in the other half of the deck must equal y, and the value of red cards in the other half of the deck must equal x meaning that "there will always be as many red cards in the first half of the deck as there are black cards in the second half of the deck."

==16. Suppose that each daughter in your family has the same number of brothers as she has sisters, and each son in your family has twice as many sisters as he has brothers. How many sons and daughters are in the family?==

Answer:3 total, 2 sister and 1 brother
Solution: Since the daughters in the family each have as many brothers as sisters the amount of sisters, with x standing for the amount of brothers, is x+1. As each brother has twice as many sisters as brothers, the amount of sisters must equal 2(x-1) or 2x-2. To find the number of brother: x+1=2x+1, 1=x-2, 3=x, which means that their are 3 brothers and 4 sisters (x+1= the number of sisters and x=3). This makes sense because a sister would have an equal amount of brothers to sisters, 3 sisters and 3 brothers, if there were 4 sisters and 3 brothers total, and each brother would have 4 sisters and 3 brothers, which is twice the amount of brothers to sisters.

==17~21==
==Audrey Chen==

==17.The zero point on a bathroom scale is set incorrectly, but otherwise the scale is accurate. It shows 60 kg when Dan stands on the scale, 50 kg when Sarah stands on the scale, but 105 kg when Dan and Sarah both stand on the scale. Does the scale read too high or too low? Explain. ==

''The scale read too low, since Dan is shown as 60kg and Sarah is 50kg, suppose 60+50=110, 105-110=-5, so that means the scale is smaller than 0 in the beginning''

==18. Alice takes one-third of the pennies from a large jar. Then Bret takes one-third of the remaining pennies from the jar. Finally, Carla takes one-third of the remaining pennies from the jar, leaving 40 pennies in the jar. How many pennies were in the jar at the start? ==

''If the total pennies is "x", Alice take 1/3x, so it has 2/3x left after Alice took it, than Bret take 1/3 out, after Alice took it, which is 2/3x*1/3= 2/9x, so in the beginning they have x, after Alice took it, it has 2/3x left, and Bret took 2/9x, so after Bret took it, it becomes 2/3x-2/9x= 4/9x-2/9x=2/9x left in the jar. Than Carla take 1/3 of the rest, so she took 1/3 of rest which is 2/9x*1/3=3/27x, so Alice took 1/3x, Bret tool 2/9x, Carla took 3/27x, three of them totaly took 1/3x+2/9x+3/27x=18/27x, so there still has x-18/27x= 9/27x= 1/3 left, 1/3x=40pennies, so x=120 pennies, so it was having 120 pennies in the jar.

==19. One morning each member of Angela's family drank an eight-ounce cup of coffee and milk, with the (nonzero) amounts of coffee and milk varying from cup to cup. Angela drank a quarter of the total amount of milk and a sixth of the total amount of coffee. What is the least number of people in the family? ==

''If we let total milk is x, total coffee is y. Than 1/4x+1/6y=8, and because every cup is 8ounce, x+y is multiple by 8. So make it easier, we use 1/4x+1/6y=8 * 12 to both sides. than we will got 3x+2y=96, now we have 3x+2y=96 and x+y is multiple of 8, and the number that multiple by 8 is 8, 16, 24, 32... so 2x+2y= 16, 32, 48, 64, 80, 96, since 3x+2y=96, it can't be more than 96. It will only have 6 possible number, so if you take 3x+2y=96 substracting 2x+2y=16, 32, 48, 64, 80, 96 you can get 6 possible x, which are 80, 64, 48, 32, 16, and 0. Than put the number into 3x+2y=96, if you put 80 in, will get 20, which is bigger than 8, and also 64, 48. If we use 32, it will equal to 8, but that means we have 0 coffee, but coffee can't be 0, so there's only 16 and 0 left. Since Angela had 1/4 of total amount of milk, milk can't be 0. So we got 16ounce than 16*(1/4)=4, so that means she had 8-4=4 's coffee. So 4=1/6 coffee, than the total amount of coffee would be 4*6=24. than x=16 and y=24, 16+24=40 40/8ounce=5, so at least have 5 cups of drinks, so that means at least they have 5 members in Angela's family.''

==20.Of two clocks next to each other, one runs 5 min per hour fast and the other runs 5 min per hour slow. At midnight the clocks show the same time. At what time are they are one hour apart? ==

''Since one clock runs 5 min faster per hour, the other is 5 min slower, after clock runs an hour, two clocks will have 10 min different from each other. 60 min an hour. 60/10=6, so after 6 hours two clocks will having one hour apart, and that would be 6AM.''

==21.Sven placed exactly in the middle among all runners in a race. Dan was slower than Sven, in 10th place, and Lars was in 16th place. How many runners were in the race? ==

''There were 17 runners. Since lars was in 16th place, the runners at least have to be 16, than if Sven is placed exactly in the middle, it means it would have even number of runners. Because Dan is slower and he was at 10 place that tells us Seven has to be before 10th, and if there has 19 runners, Sven and Dan would be at the same place, so it should be 17 runners, than Sven would be at exactly in the middle which at 9th place.''

==22-25==

Roland Will

22. During a vacation, it rained on 13 days, but when it rained in the morning, the afternoon was sunny, and every rainy afternoon was preceded by a sunny morning. There were 11 sunny mornings and 12 sunny afternoons. How long was the vacation?

Answer: 18 days of vacation.

Solution: 13 of the days of vacation were half sunny and half rainy. As there were 23 sunny mornings and afternoons (11 sunny mornings+12 sunny afternoons = 23 sunny mornings and afternoons), 13 of those sunny afternoons or mornings were on half rainy days. This means there are 10 sunny half-days left over, which equal 5 sunny full days. The 5 sunny full days plus the 13 half sunny/rainy days equal 18 total days of vacation.

23. Suppose you overhear the following conversation: Paul: How old are your three children? Paula: The product of their ages is 36 and the sum of their ages is the same as today's date. Paul: That is not enough information. Paula: The oldest child also has red hair. If you were Paul could you determine the ages of Paula's children? Explain.

Answer: If I were Paul this might be possible, but since we don’t know the date that Paula said this, it is not possible for us to find out.

Solution: There are many different combinations of three numbers that can be multiplied and will produce 36. As we do not know the date that Paula said this, the only thing we can be sure of is that the sum of the ages is less than 31 because no month has more than 31 days. Unfortunately, only one set of ages (ages 1 year old, 1 year old and 36 years old) has a sum greater than 31, which leaves many possible combinations open as possible. For today’s date, the 13th, ages of 2, 2, and 9 would produce 36 and have a sum of 13, but, again, it is uncertain. If it were the first of the month, there would be no possible combinations that would produce 36 and sum 1.

24. Two candles of equal length were lit at the same time. One candle took 6 hr to burn out and the other candle took 3 hr to burn out. After how much time was one candle exactly twice as long as the other candle?

Answer: 2 hours.

Solution: The faster burning candle took half the time to burn as the slower burning candle (3 hours/ 6 hours = 1/2), meaning it burned twice as fast. This means that after 2/3 of the total burning time for the faster burning candle it will be 1/3 of its original height and at the slower burning candle will be at 2/3 of its original height and 1/3 is half of 2/3. Since the faster burning candle took 3 hours to burn, 2/3 of its total burning time is 2 hours.

25. Two candles of length L and L + 1 were lit at 6:00 and 4:30, respectively. At 8:30 they had the same length. The longer candle died at 10:30 and the shorter candle died at 10:00. Find L.

Answer: L=2.

Solution: The shorter candle lasted for 4 hours and the longer candle lasted for 6 hours. As 6 hours – 4 hours = 2 hours and 2 hours / 4 hours = 1/2, the longer candle lasted 50% longer and was, therefore, 50% longer in length. This means that the +1 in L+1 on the longer candle was 1/2 of L. 1/2L=1, so L=2*1, L=2.

Course:MATH110/Archive/2010-2011/003/Groups/Group 18

2010-11-12T05:25:47Z

RolandWill: /* 14 One day in the maternity ward, the name tags for four girl babies became mixed up. (i) In how many different ways could two of the babies be tagged correctly and two of the babies be tagged incorrectly? (ii) In how many different ways could th

{{Infobox MATH110 Groups
| group number = 18
| member 1 = [[User:ChouJuChen|Audrey Chen]]
| member 2 = [[User:SifatHasan|Sifat Hasan]]
| member 3 = [[User:CaitlinLastiwkaFarquharson|Caitlin Lastiwka-Farquharson]]
| member 4 = [[User:VictoriaWall|Victoria Wall]]
| member 5 = [[User:RolandWill|Roland Will]]
| member 6 =
}}

==Sub-Pages==

Basic Skills Project [http://wiki.ubc.ca/Course:MATH110/003/Groups/Group_18/Basic_Skills_Project]

==Homework due October 20th, 2010==

I created a page for our homework due tomorrow: [http://wiki.ubc.ca/Course:MATH110/003/Groups/Group_18/Homework_October_20th,_2010 http://wiki.ubc.ca/Course:MATH110/003/Groups/Group 18/Homework October 20th, 2010]

-Roland

I've moved the page, it was missing the ''Course:'' part which means it was created directly inside the wiki and not as a subpage of your group page, which is something the wiki admins don't like that much. By the way, you're allowed to use spaces in the name of your pages.

-- [[User:DavidKohler|DavidKohler]] 06:28, 20 October 2010 (UTC)

1-5

Victoria Wall

1.A bus traveled from the terminal to the airport at an average speed of 30 mi/hr and the trip took an hour and 20 min. The bus then traveled from the airport back to the terminal and again averaged 30 mi/hr. However, the return trip required 80 min. Explain.

' 'Lets call the terminal T and the airport A. If the bus travelled from T to A at 30mi/hr and it took them one hour and 20 mins to get from T to A at this speed, and there are 60 minutes in one hour, it took the bus 60min + 20min to get to A which is a total of 80min. The bus took 80 min to get from T to A. To get from A to T at the same speed (30mi/hr) it took the bus 80min. 80min = 80 min. This means going from A to T or vis versa at 30 mi/hr it will take the bus 80min.

2.A lady did not have her driver's license with her when she failed to stop at a stop sign and then went three blocks down a one-way street the wrong way. A policeman saw her, but he did not stop her. Explain.

' 'The lady was walking. It never says she was driving.

3.One of three boxes contains apples, another box contains oranges, and another box contains a mixture of apples and oranges. The boxes are labeled APPLES, ORANGES and APPLES AND ORANGES, but each label is incorrect. Can you select one fruit from only one box and determine the correct labels? Explain.

' 'if you selecet from the box APPLES AND ORANGES then you will be able to see the labels if they are correct or not.

4.I am the brother of the blind fiddler, but brothers I have none. How can this be?

' 'Since it says that he is the brother of the blind fiddler it does not mean that the fiddle is male, since he has no brothers than the fiddler must be a female.

5.Two quarters rest next to each other on a table. One coin is held fixed while the second coin is rolled around the edge of the first coin with no slipping. When the moving coin returns to its original position, how many times has it revolved?

' 'This is because the moving quarters revolves two full revolutions

6-10

Caitlin Lastiwka- Farquharson

6. Three kinds of apples are all mixed up in a basket. How many apples must you draw without (without looking) from the basket to be sure of getting at least two of a kind?

' ' To be sure you are getting at least two of a kind, you must select all of the other types of apples, plus two more. Meaning that only once you have selected all of the other apples can you be sure that you will select two of the kind you desire. It can be written like this: x,a x2, b and x3, c, with x representing the quantity of apples. This can be calculated by x2 + x3 +2. X2 representing one of the types of apples, x3 representing the other type and 2 representing 2 of the kind of apples you are trying to select. This is the only way to be sure you are getting at least two of a kind. ' '

7. Suppose you have 40 blue socks and 40 brown socks in a drawer. How many socks must you take from the drawer (without looking) to be sure of getting (i) a pair of the same colour, and (ii) a pair with different colors.

' 'You must take three socks from the drawer to ensure you have a pair that match. This is because if you only select two, one could be brown and one could be blue. Selecting three, ensures that at least two of them will be the same colour. As for part two, you would need to select 41 socks to ensure you had a pair of different coloured socks because if you select 40 or less you could get all the same colour, but selecting 41 ensures you will have at least one pair of mixed colour. ' '

8. Rueben says "Two days ago I was 20 years old. Later next year I will be 23 years old." Explain how this is possible.

' 'It is possible if your birthday is on the 31st of December and today is the 1st of January. This is because on the 30th of December (two days ago) you we’re 20 years old and now you are 21, later this year you will turn 22 on the 31st of December, and therefore 23 the next year.' '

9. A rope ladder hanging over the side of a boat has rungs one foot apart. Ten rungs are showing. If the tide rises five feet, how many rungs will be showing?

' ' 5 rungs will be showing, because if there are 10 showing now, and they are each a foot apart, then for 5 more rungs to be showing there would need to be an increase in the level of water by 5 feet. ' '

10.Suppose one-half of all people are chocolate eaters and one-half of all people are women. (i) Does it follow that one-fourth of all people are women chocolate eaters? (ii) Does it follow that one-half of all men are chocolate eaters? Explain.

' ' No, it does not follow that one-fourth of all people are women chocolate eaters and it does not follow that half of all men are chocolate eaters because are completely independent scenarios. Meaning that the the amount of women there are does not influence the amount of men that will eat chocolate. For example, If 50% of people are women and 50% of the entire population including men and women eat chocolate (arrived at by using the same logic that if 1/4 of women eat chocolate and 1/4 of men eat chocolate), that entire 50% could be comprised of women, meaning that no men eat chocolate disproving the statement.

11-14

Sifat Hasan

11. A woman, her older brother, her son, and her daughter are chess players. The worst player’s twin, who is one of the four players, and the best player are of opposite sex. The worst player and the best player have the same age. If this is possible, who is the worst player?

The four players (according to age, from oldest to youngest) are: woman's older brother, woman, and the son and the daughter (of the same age). Assuming that the children are of the same age (i.e. twins), the worst player is one of them, since they are the only ones who can have a twin. Assuming that the worst player is the daughter, her brother the son, is of the opposite sex as the woman, therefore the woman is the worst player. However, since the worst and the best player are of the same age, this is not possible, because the twins are of the opposite sex and they are of different genders.

12 A Manhattan fellow had a girlfriend in the Bronx and a girlfriend in Brooklyn. He decided which girlfriend to visit by arriving randomly at the train station and taking the first of the Bronx or Brooklyn trains that arrived. The trains to Brooklyn and the Bronx each arrived regularly every 10 minutes. Not long after he began his scheme the man's Bronx girlfriend left him because he rarely visited. Give a (logical) explanation

Assuming that the Bronx and the Brooklyn train arrive one after the other every 10 minutes, the only logical explanation would be that the man in Manhattan coincidentally went to the station 10 minutes or less before a train to Brooklyn arrived, most of the time.

13 If a clock takes 5 seconds to strike 5:00 (with 5 equally spaced chimes), how long does it take to strike 10:00 (with 10 equally spaced chimes)?

If it takes 5 seconds to strike 5, there will be 4 little halts in the middle. Therefore it takes 5 chimes 4 (5/4) = 1.25 second halts to finish. For 10 chimes, there are 9 halts so, it takes 9x 1.25 = 11.25 seconds for 10 halts.

14 One day in the maternity ward, the name tags for four girl babies became mixed up. (i) In how many different ways could two of the babies be tagged correctly and two of the babies be tagged incorrectly? (ii) In how many different ways could three of the babies be tagged correctly and one baby be tagged incorrectly?

(i)and (ii) If we take the babies names as A,B,C and D. There are 6 different combinations of the mix up, that two babies' names can be correct and 2 can be wrong. Assuming the name tags for the babies A,B,C and D are in respective order, they are ABDC, ADCB, ACBD, DBCA, CBAD and BACD. All other combinations for example BCAD will have one correct and 3 incorrect, or all four of them correct, because if 3 are correct, the fourth one has to be correct.

==15-16==
==Roland Will==

==15. Alex says to you, “I'll bet you any amount of money that if I shuffle this deck of cards, there will always be as many red cards in the first half of the deck as there are black cards in the second half of the deck.” Should you accept his bet?==

Answer: No, you shouldn't assuming the deck has equal amounts of red and black cards as in a standard 52 card deck.
Solution: In a standard 52 card deck, half of the cards (26) are black and half are red. If you take 26 cards at random from the deck, x of them will be black and y of them will be red, and x+y=26. As there are 26 of each color in the deck, then x+?=26 for the black cards in the deck and ?+y=26 for the red cards in the deck. As x+y=26 in the first randomly selected 26 cards, then the value of black cards in the other half of the deck must equal y, and the value of red cards in the other half of the deck must equal x meaning that "there will always be as many red cards in the first half of the deck as there are black cards in the second half of the deck."

==16. Suppose that each daughter in your family has the same number of brothers as she has sisters, and each son in your family has twice as many sisters as he has brothers. How many sons and daughters are in the family?==

Answer:3 total, 2 sister and 1 brother
Solution: Since the daughters in the family each have as many brothers as sisters the amount of sisters, with x standing for the amount of brothers, is x+1. As each brother has twice as many sisters as brothers, the amount of sisters must equal 2(x-1) or 2x-2. To find the number of brother: x+1=2x+1, 1=x-2, 3=x, which means that their are 3 brothers and 4 sisters (x+1= the number of sisters and x=3). This makes sense because a sister would have an equal amount of brothers to sisters, 3 sisters and 3 brothers, if there were 4 sisters and 3 brothers total, and each brother would have 4 sisters and 3 brothers, which is twice the amount of brothers to sisters.

==17~21==
==Audrey Chen==

==17.The zero point on a bathroom scale is set incorrectly, but otherwise the scale is accurate. It shows 60 kg when Dan stands on the scale, 50 kg when Sarah stands on the scale, but 105 kg when Dan and Sarah both stand on the scale. Does the scale read too high or too low? Explain. ==

''The scale read too low, since Dan is shown as 60kg and Sarah is 50kg, suppose 60+50=110, 105-110=-5, so that means the scale is smaller than 0 in the beginning''

==18. Alice takes one-third of the pennies from a large jar. Then Bret takes one-third of the remaining pennies from the jar. Finally, Carla takes one-third of the remaining pennies from the jar, leaving 40 pennies in the jar. How many pennies were in the jar at the start? ==

''If the total pennies is "x", Alice take 1/3x, so it has 2/3x left after Alice took it, than Bret take 1/3 out, after Alice took it, which is 2/3x*1/3= 2/9x, so in the beginning they have x, after Alice took it, it has 2/3x left, and Bret took 2/9x, so after Bret took it, it becomes 2/3x-2/9x= 4/9x-2/9x=2/9x left in the jar. Than Carla take 1/3 of the rest, so she took 1/3 of rest which is 2/9x*1/3=3/27x, so Alice took 1/3x, Bret tool 2/9x, Carla took 3/27x, three of them totaly took 1/3x+2/9x+3/27x=18/27x, so there still has x-18/27x= 9/27x= 1/3 left, 1/3x=40pennies, so x=120 pennies, so it was having 120 pennies in the jar.

==19. One morning each member of Angela's family drank an eight-ounce cup of coffee and milk, with the (nonzero) amounts of coffee and milk varying from cup to cup. Angela drank a quarter of the total amount of milk and a sixth of the total amount of coffee. What is the least number of people in the family? ==

''If we let total milk is x, total coffee is y. Than 1/4x+1/6y=8, and because every cup is 8ounce, x+y is multiple by 8. So make it easier, we use 1/4x+1/6y=8 * 12 to both sides. than we will got 3x+2y=96, now we have 3x+2y=96 and x+y is multiple of 8, and the number that multiple by 8 is 8, 16, 24, 32... so 2x+2y= 16, 32, 48, 64, 80, 96, since 3x+2y=96, it can't be more than 96. It will only have 6 possible number, so if you take 3x+2y=96 substracting 2x+2y=16, 32, 48, 64, 80, 96 you can get 6 possible x, which are 80, 64, 48, 32, 16, and 0. Than put the number into 3x+2y=96, if you put 80 in, will get 20, which is bigger than 8, and also 64, 48. If we use 32, it will equal to 8, but that means we have 0 coffee, but coffee can't be 0, so there's only 16 and 0 left. Since Angela had 1/4 of total amount of milk, milk can't be 0. So we got 16ounce than 16*(1/4)=4, so that means she had 8-4=4 's coffee. So 4=1/6 coffee, than the total amount of coffee would be 4*6=24. than x=16 and y=24, 16+24=40 40/8ounce=5, so at least have 5 cups of drinks, so that means at least they have 5 members in Angela's family.''

==20.Of two clocks next to each other, one runs 5 min per hour fast and the other runs 5 min per hour slow. At midnight the clocks show the same time. At what time are they are one hour apart? ==

''Since one clock runs 5 min faster per hour, the other is 5 min slower, after clock runs an hour, two clocks will have 10 min different from each other. 60 min an hour. 60/10=6, so after 6 hours two clocks will having one hour apart, and that would be 6AM.''

==21.Sven placed exactly in the middle among all runners in a race. Dan was slower than Sven, in 10th place, and Lars was in 16th place. How many runners were in the race? ==

''There were 17 runners. Since lars was in 16th place, the runners at least have to be 16, than if Sven is placed exactly in the middle, it means it would have even number of runners. Because Dan is slower and he was at 10 place that tells us Seven has to be before 10th, and if there has 19 runners, Sven and Dan would be at the same place, so it should be 17 runners, than Sven would be at exactly in the middle which at 9th place.''

==22-25==

Roland Will

22. During a vacation, it rained on 13 days, but when it rained in the morning, the afternoon was sunny, and every rainy afternoon was preceded by a sunny morning. There were 11 sunny mornings and 12 sunny afternoons. How long was the vacation?

Answer: 18 days of vacation.

Solution: 13 of the days of vacation were half sunny and half rainy. As there were 23 sunny mornings and afternoons (11 sunny mornings+12 sunny afternoons = 23 sunny mornings and afternoons), 13 of those sunny afternoons or mornings were on half rainy days. This means there are 10 sunny half-days left over, which equal 5 sunny full days. The 5 sunny full days plus the 13 half sunny/rainy days equal 18 total days of vacation.

23. Suppose you overhear the following conversation: Paul: How old are your three children? Paula: The product of their ages is 36 and the sum of their ages is the same as today's date. Paul: That is not enough information. Paula: The oldest child also has red hair. If you were Paul could you determine the ages of Paula's children? Explain.

Answer: If I were Paul this might be possible, but since we don’t know the date that Paula said this, it is not possible for us to find out.

Solution: There are many different combinations of three numbers that can be multiplied and will produce 36. As we do not know the date that Paula said this, the only thing we can be sure of is that the sum of the ages is less than 31 because no month has more than 31 days. Unfortunately, only one set of ages (ages 1 year old, 1 year old and 36 years old) has a sum greater than 31, which leaves many possible combinations open as possible. For today’s date, the 13th, ages of 2, 2, and 9 would produce 36 and have a sum of 13, but, again, it is uncertain. If it were the first of the month, there would be no possible combinations that would produce 36 and sum 1.

24. Two candles of equal length were lit at the same time. One candle took 6 hr to burn out and the other candle took 3 hr to burn out. After how much time was one candle exactly twice as long as the other candle?

Answer: 2 hours.

Solution: The faster burning candle took half the time to burn as the slower burning candle (3 hours/ 6 hours = 1/2), meaning it burned twice as fast. This means that after 2/3 of the total burning time for the faster burning candle it will be 1/3 of its original height and at the slower burning candle will be at 2/3 of its original height and 1/3 is half of 2/3. Since the faster burning candle took 3 hours to burn, 2/3 of its total burning time is 2 hours.

25. Two candles of length L and L + 1 were lit at 6:00 and 4:30, respectively. At 8:30 they had the same length. The longer candle died at 10:30 and the shorter candle died at 10:00. Find L.

Answer: L=2.

Solution: The shorter candle lasted for 4 hours and the longer candle lasted for 6 hours. As 6 hours – 4 hours = 2 hours and 2 hours / 4 hours = 1/2, the longer candle lasted 50% longer and was, therefore, 50% longer in length. This means that the +1 in L+1 on the longer candle was 1/2 of L. 1/2L=1, so L=2*1, L=2.

Course:MATH110/Archive/2010-2011/003/Groups/Group 18

2010-11-12T05:25:38Z

RolandWill: /* 13 If a clock takes 5 seconds to strike 5:00 (with 5 equally spaced chimes), how long does it take to strike 10:00 (with 10 equally spaced chimes)? */

{{Infobox MATH110 Groups
| group number = 18
| member 1 = [[User:ChouJuChen|Audrey Chen]]
| member 2 = [[User:SifatHasan|Sifat Hasan]]
| member 3 = [[User:CaitlinLastiwkaFarquharson|Caitlin Lastiwka-Farquharson]]
| member 4 = [[User:VictoriaWall|Victoria Wall]]
| member 5 = [[User:RolandWill|Roland Will]]
| member 6 =
}}

==Sub-Pages==

Basic Skills Project [http://wiki.ubc.ca/Course:MATH110/003/Groups/Group_18/Basic_Skills_Project]

==Homework due October 20th, 2010==

I created a page for our homework due tomorrow: [http://wiki.ubc.ca/Course:MATH110/003/Groups/Group_18/Homework_October_20th,_2010 http://wiki.ubc.ca/Course:MATH110/003/Groups/Group 18/Homework October 20th, 2010]

-Roland

I've moved the page, it was missing the ''Course:'' part which means it was created directly inside the wiki and not as a subpage of your group page, which is something the wiki admins don't like that much. By the way, you're allowed to use spaces in the name of your pages.

-- [[User:DavidKohler|DavidKohler]] 06:28, 20 October 2010 (UTC)

1-5

Victoria Wall

1.A bus traveled from the terminal to the airport at an average speed of 30 mi/hr and the trip took an hour and 20 min. The bus then traveled from the airport back to the terminal and again averaged 30 mi/hr. However, the return trip required 80 min. Explain.

' 'Lets call the terminal T and the airport A. If the bus travelled from T to A at 30mi/hr and it took them one hour and 20 mins to get from T to A at this speed, and there are 60 minutes in one hour, it took the bus 60min + 20min to get to A which is a total of 80min. The bus took 80 min to get from T to A. To get from A to T at the same speed (30mi/hr) it took the bus 80min. 80min = 80 min. This means going from A to T or vis versa at 30 mi/hr it will take the bus 80min.

2.A lady did not have her driver's license with her when she failed to stop at a stop sign and then went three blocks down a one-way street the wrong way. A policeman saw her, but he did not stop her. Explain.

' 'The lady was walking. It never says she was driving.

3.One of three boxes contains apples, another box contains oranges, and another box contains a mixture of apples and oranges. The boxes are labeled APPLES, ORANGES and APPLES AND ORANGES, but each label is incorrect. Can you select one fruit from only one box and determine the correct labels? Explain.

' 'if you selecet from the box APPLES AND ORANGES then you will be able to see the labels if they are correct or not.

4.I am the brother of the blind fiddler, but brothers I have none. How can this be?

' 'Since it says that he is the brother of the blind fiddler it does not mean that the fiddle is male, since he has no brothers than the fiddler must be a female.

5.Two quarters rest next to each other on a table. One coin is held fixed while the second coin is rolled around the edge of the first coin with no slipping. When the moving coin returns to its original position, how many times has it revolved?

' 'This is because the moving quarters revolves two full revolutions

6-10

Caitlin Lastiwka- Farquharson

6. Three kinds of apples are all mixed up in a basket. How many apples must you draw without (without looking) from the basket to be sure of getting at least two of a kind?

' ' To be sure you are getting at least two of a kind, you must select all of the other types of apples, plus two more. Meaning that only once you have selected all of the other apples can you be sure that you will select two of the kind you desire. It can be written like this: x,a x2, b and x3, c, with x representing the quantity of apples. This can be calculated by x2 + x3 +2. X2 representing one of the types of apples, x3 representing the other type and 2 representing 2 of the kind of apples you are trying to select. This is the only way to be sure you are getting at least two of a kind. ' '

7. Suppose you have 40 blue socks and 40 brown socks in a drawer. How many socks must you take from the drawer (without looking) to be sure of getting (i) a pair of the same colour, and (ii) a pair with different colors.

' 'You must take three socks from the drawer to ensure you have a pair that match. This is because if you only select two, one could be brown and one could be blue. Selecting three, ensures that at least two of them will be the same colour. As for part two, you would need to select 41 socks to ensure you had a pair of different coloured socks because if you select 40 or less you could get all the same colour, but selecting 41 ensures you will have at least one pair of mixed colour. ' '

8. Rueben says "Two days ago I was 20 years old. Later next year I will be 23 years old." Explain how this is possible.

' 'It is possible if your birthday is on the 31st of December and today is the 1st of January. This is because on the 30th of December (two days ago) you we’re 20 years old and now you are 21, later this year you will turn 22 on the 31st of December, and therefore 23 the next year.' '

9. A rope ladder hanging over the side of a boat has rungs one foot apart. Ten rungs are showing. If the tide rises five feet, how many rungs will be showing?

' ' 5 rungs will be showing, because if there are 10 showing now, and they are each a foot apart, then for 5 more rungs to be showing there would need to be an increase in the level of water by 5 feet. ' '

10.Suppose one-half of all people are chocolate eaters and one-half of all people are women. (i) Does it follow that one-fourth of all people are women chocolate eaters? (ii) Does it follow that one-half of all men are chocolate eaters? Explain.

' ' No, it does not follow that one-fourth of all people are women chocolate eaters and it does not follow that half of all men are chocolate eaters because are completely independent scenarios. Meaning that the the amount of women there are does not influence the amount of men that will eat chocolate. For example, If 50% of people are women and 50% of the entire population including men and women eat chocolate (arrived at by using the same logic that if 1/4 of women eat chocolate and 1/4 of men eat chocolate), that entire 50% could be comprised of women, meaning that no men eat chocolate disproving the statement.

11-14

Sifat Hasan

11. A woman, her older brother, her son, and her daughter are chess players. The worst player’s twin, who is one of the four players, and the best player are of opposite sex. The worst player and the best player have the same age. If this is possible, who is the worst player?

The four players (according to age, from oldest to youngest) are: woman's older brother, woman, and the son and the daughter (of the same age). Assuming that the children are of the same age (i.e. twins), the worst player is one of them, since they are the only ones who can have a twin. Assuming that the worst player is the daughter, her brother the son, is of the opposite sex as the woman, therefore the woman is the worst player. However, since the worst and the best player are of the same age, this is not possible, because the twins are of the opposite sex and they are of different genders.

12 A Manhattan fellow had a girlfriend in the Bronx and a girlfriend in Brooklyn. He decided which girlfriend to visit by arriving randomly at the train station and taking the first of the Bronx or Brooklyn trains that arrived. The trains to Brooklyn and the Bronx each arrived regularly every 10 minutes. Not long after he began his scheme the man's Bronx girlfriend left him because he rarely visited. Give a (logical) explanation

Assuming that the Bronx and the Brooklyn train arrive one after the other every 10 minutes, the only logical explanation would be that the man in Manhattan coincidentally went to the station 10 minutes or less before a train to Brooklyn arrived, most of the time.

13 If a clock takes 5 seconds to strike 5:00 (with 5 equally spaced chimes), how long does it take to strike 10:00 (with 10 equally spaced chimes)?

If it takes 5 seconds to strike 5, there will be 4 little halts in the middle. Therefore it takes 5 chimes 4 (5/4) = 1.25 second halts to finish. For 10 chimes, there are 9 halts so, it takes 9x 1.25 = 11.25 seconds for 10 halts.

==14 One day in the maternity ward, the name tags for four girl babies became mixed up. (i) In how many different ways could two of the babies be tagged correctly and two of the babies be tagged incorrectly? (ii) In how many different ways could three of the babies be tagged correctly and one baby be tagged incorrectly?==

(i)and (ii) If we take the babies names as A,B,C and D. There are 6 different combinations of the mix up, that two babies' names can be correct and 2 can be wrong. Assuming the name tags for the babies A,B,C and D are in respective order, they are ABDC, ADCB, ACBD, DBCA, CBAD and BACD. All other combinations for example BCAD will have one correct and 3 incorrect, or all four of them correct, because if 3 are correct, the fourth one has to be correct.

==15-16==
==Roland Will==

==15. Alex says to you, “I'll bet you any amount of money that if I shuffle this deck of cards, there will always be as many red cards in the first half of the deck as there are black cards in the second half of the deck.” Should you accept his bet?==

Answer: No, you shouldn't assuming the deck has equal amounts of red and black cards as in a standard 52 card deck.
Solution: In a standard 52 card deck, half of the cards (26) are black and half are red. If you take 26 cards at random from the deck, x of them will be black and y of them will be red, and x+y=26. As there are 26 of each color in the deck, then x+?=26 for the black cards in the deck and ?+y=26 for the red cards in the deck. As x+y=26 in the first randomly selected 26 cards, then the value of black cards in the other half of the deck must equal y, and the value of red cards in the other half of the deck must equal x meaning that "there will always be as many red cards in the first half of the deck as there are black cards in the second half of the deck."

==16. Suppose that each daughter in your family has the same number of brothers as she has sisters, and each son in your family has twice as many sisters as he has brothers. How many sons and daughters are in the family?==

Answer:3 total, 2 sister and 1 brother
Solution: Since the daughters in the family each have as many brothers as sisters the amount of sisters, with x standing for the amount of brothers, is x+1. As each brother has twice as many sisters as brothers, the amount of sisters must equal 2(x-1) or 2x-2. To find the number of brother: x+1=2x+1, 1=x-2, 3=x, which means that their are 3 brothers and 4 sisters (x+1= the number of sisters and x=3). This makes sense because a sister would have an equal amount of brothers to sisters, 3 sisters and 3 brothers, if there were 4 sisters and 3 brothers total, and each brother would have 4 sisters and 3 brothers, which is twice the amount of brothers to sisters.

==17~21==
==Audrey Chen==

==17.The zero point on a bathroom scale is set incorrectly, but otherwise the scale is accurate. It shows 60 kg when Dan stands on the scale, 50 kg when Sarah stands on the scale, but 105 kg when Dan and Sarah both stand on the scale. Does the scale read too high or too low? Explain. ==

''The scale read too low, since Dan is shown as 60kg and Sarah is 50kg, suppose 60+50=110, 105-110=-5, so that means the scale is smaller than 0 in the beginning''

==18. Alice takes one-third of the pennies from a large jar. Then Bret takes one-third of the remaining pennies from the jar. Finally, Carla takes one-third of the remaining pennies from the jar, leaving 40 pennies in the jar. How many pennies were in the jar at the start? ==

''If the total pennies is "x", Alice take 1/3x, so it has 2/3x left after Alice took it, than Bret take 1/3 out, after Alice took it, which is 2/3x*1/3= 2/9x, so in the beginning they have x, after Alice took it, it has 2/3x left, and Bret took 2/9x, so after Bret took it, it becomes 2/3x-2/9x= 4/9x-2/9x=2/9x left in the jar. Than Carla take 1/3 of the rest, so she took 1/3 of rest which is 2/9x*1/3=3/27x, so Alice took 1/3x, Bret tool 2/9x, Carla took 3/27x, three of them totaly took 1/3x+2/9x+3/27x=18/27x, so there still has x-18/27x= 9/27x= 1/3 left, 1/3x=40pennies, so x=120 pennies, so it was having 120 pennies in the jar.

==19. One morning each member of Angela's family drank an eight-ounce cup of coffee and milk, with the (nonzero) amounts of coffee and milk varying from cup to cup. Angela drank a quarter of the total amount of milk and a sixth of the total amount of coffee. What is the least number of people in the family? ==

''If we let total milk is x, total coffee is y. Than 1/4x+1/6y=8, and because every cup is 8ounce, x+y is multiple by 8. So make it easier, we use 1/4x+1/6y=8 * 12 to both sides. than we will got 3x+2y=96, now we have 3x+2y=96 and x+y is multiple of 8, and the number that multiple by 8 is 8, 16, 24, 32... so 2x+2y= 16, 32, 48, 64, 80, 96, since 3x+2y=96, it can't be more than 96. It will only have 6 possible number, so if you take 3x+2y=96 substracting 2x+2y=16, 32, 48, 64, 80, 96 you can get 6 possible x, which are 80, 64, 48, 32, 16, and 0. Than put the number into 3x+2y=96, if you put 80 in, will get 20, which is bigger than 8, and also 64, 48. If we use 32, it will equal to 8, but that means we have 0 coffee, but coffee can't be 0, so there's only 16 and 0 left. Since Angela had 1/4 of total amount of milk, milk can't be 0. So we got 16ounce than 16*(1/4)=4, so that means she had 8-4=4 's coffee. So 4=1/6 coffee, than the total amount of coffee would be 4*6=24. than x=16 and y=24, 16+24=40 40/8ounce=5, so at least have 5 cups of drinks, so that means at least they have 5 members in Angela's family.''

==20.Of two clocks next to each other, one runs 5 min per hour fast and the other runs 5 min per hour slow. At midnight the clocks show the same time. At what time are they are one hour apart? ==

''Since one clock runs 5 min faster per hour, the other is 5 min slower, after clock runs an hour, two clocks will have 10 min different from each other. 60 min an hour. 60/10=6, so after 6 hours two clocks will having one hour apart, and that would be 6AM.''

==21.Sven placed exactly in the middle among all runners in a race. Dan was slower than Sven, in 10th place, and Lars was in 16th place. How many runners were in the race? ==

''There were 17 runners. Since lars was in 16th place, the runners at least have to be 16, than if Sven is placed exactly in the middle, it means it would have even number of runners. Because Dan is slower and he was at 10 place that tells us Seven has to be before 10th, and if there has 19 runners, Sven and Dan would be at the same place, so it should be 17 runners, than Sven would be at exactly in the middle which at 9th place.''

==22-25==

Roland Will

22. During a vacation, it rained on 13 days, but when it rained in the morning, the afternoon was sunny, and every rainy afternoon was preceded by a sunny morning. There were 11 sunny mornings and 12 sunny afternoons. How long was the vacation?

Answer: 18 days of vacation.

Solution: 13 of the days of vacation were half sunny and half rainy. As there were 23 sunny mornings and afternoons (11 sunny mornings+12 sunny afternoons = 23 sunny mornings and afternoons), 13 of those sunny afternoons or mornings were on half rainy days. This means there are 10 sunny half-days left over, which equal 5 sunny full days. The 5 sunny full days plus the 13 half sunny/rainy days equal 18 total days of vacation.

23. Suppose you overhear the following conversation: Paul: How old are your three children? Paula: The product of their ages is 36 and the sum of their ages is the same as today's date. Paul: That is not enough information. Paula: The oldest child also has red hair. If you were Paul could you determine the ages of Paula's children? Explain.

Answer: If I were Paul this might be possible, but since we don’t know the date that Paula said this, it is not possible for us to find out.

Solution: There are many different combinations of three numbers that can be multiplied and will produce 36. As we do not know the date that Paula said this, the only thing we can be sure of is that the sum of the ages is less than 31 because no month has more than 31 days. Unfortunately, only one set of ages (ages 1 year old, 1 year old and 36 years old) has a sum greater than 31, which leaves many possible combinations open as possible. For today’s date, the 13th, ages of 2, 2, and 9 would produce 36 and have a sum of 13, but, again, it is uncertain. If it were the first of the month, there would be no possible combinations that would produce 36 and sum 1.

24. Two candles of equal length were lit at the same time. One candle took 6 hr to burn out and the other candle took 3 hr to burn out. After how much time was one candle exactly twice as long as the other candle?

Answer: 2 hours.

Solution: The faster burning candle took half the time to burn as the slower burning candle (3 hours/ 6 hours = 1/2), meaning it burned twice as fast. This means that after 2/3 of the total burning time for the faster burning candle it will be 1/3 of its original height and at the slower burning candle will be at 2/3 of its original height and 1/3 is half of 2/3. Since the faster burning candle took 3 hours to burn, 2/3 of its total burning time is 2 hours.

25. Two candles of length L and L + 1 were lit at 6:00 and 4:30, respectively. At 8:30 they had the same length. The longer candle died at 10:30 and the shorter candle died at 10:00. Find L.

Answer: L=2.

Solution: The shorter candle lasted for 4 hours and the longer candle lasted for 6 hours. As 6 hours – 4 hours = 2 hours and 2 hours / 4 hours = 1/2, the longer candle lasted 50% longer and was, therefore, 50% longer in length. This means that the +1 in L+1 on the longer candle was 1/2 of L. 1/2L=1, so L=2*1, L=2.

Course:MATH110/Archive/2010-2011/003/Groups/Group 18

2010-11-12T05:25:27Z

RolandWill: /* 12 A Manhattan fellow had a girlfriend in the Bronx and a girlfriend in Brooklyn. He decided which girlfriend to visit by arriving randomly at the train station and taking the first of the Bronx or Brooklyn trains that arrived. The trains to Brook

{{Infobox MATH110 Groups
| group number = 18
| member 1 = [[User:ChouJuChen|Audrey Chen]]
| member 2 = [[User:SifatHasan|Sifat Hasan]]
| member 3 = [[User:CaitlinLastiwkaFarquharson|Caitlin Lastiwka-Farquharson]]
| member 4 = [[User:VictoriaWall|Victoria Wall]]
| member 5 = [[User:RolandWill|Roland Will]]
| member 6 =
}}

==Sub-Pages==

Basic Skills Project [http://wiki.ubc.ca/Course:MATH110/003/Groups/Group_18/Basic_Skills_Project]

==Homework due October 20th, 2010==

I created a page for our homework due tomorrow: [http://wiki.ubc.ca/Course:MATH110/003/Groups/Group_18/Homework_October_20th,_2010 http://wiki.ubc.ca/Course:MATH110/003/Groups/Group 18/Homework October 20th, 2010]

-Roland

I've moved the page, it was missing the ''Course:'' part which means it was created directly inside the wiki and not as a subpage of your group page, which is something the wiki admins don't like that much. By the way, you're allowed to use spaces in the name of your pages.

-- [[User:DavidKohler|DavidKohler]] 06:28, 20 October 2010 (UTC)

1-5

Victoria Wall

1.A bus traveled from the terminal to the airport at an average speed of 30 mi/hr and the trip took an hour and 20 min. The bus then traveled from the airport back to the terminal and again averaged 30 mi/hr. However, the return trip required 80 min. Explain.

' 'Lets call the terminal T and the airport A. If the bus travelled from T to A at 30mi/hr and it took them one hour and 20 mins to get from T to A at this speed, and there are 60 minutes in one hour, it took the bus 60min + 20min to get to A which is a total of 80min. The bus took 80 min to get from T to A. To get from A to T at the same speed (30mi/hr) it took the bus 80min. 80min = 80 min. This means going from A to T or vis versa at 30 mi/hr it will take the bus 80min.

2.A lady did not have her driver's license with her when she failed to stop at a stop sign and then went three blocks down a one-way street the wrong way. A policeman saw her, but he did not stop her. Explain.

' 'The lady was walking. It never says she was driving.

3.One of three boxes contains apples, another box contains oranges, and another box contains a mixture of apples and oranges. The boxes are labeled APPLES, ORANGES and APPLES AND ORANGES, but each label is incorrect. Can you select one fruit from only one box and determine the correct labels? Explain.

' 'if you selecet from the box APPLES AND ORANGES then you will be able to see the labels if they are correct or not.

4.I am the brother of the blind fiddler, but brothers I have none. How can this be?

' 'Since it says that he is the brother of the blind fiddler it does not mean that the fiddle is male, since he has no brothers than the fiddler must be a female.

5.Two quarters rest next to each other on a table. One coin is held fixed while the second coin is rolled around the edge of the first coin with no slipping. When the moving coin returns to its original position, how many times has it revolved?

' 'This is because the moving quarters revolves two full revolutions

6-10

Caitlin Lastiwka- Farquharson

6. Three kinds of apples are all mixed up in a basket. How many apples must you draw without (without looking) from the basket to be sure of getting at least two of a kind?

' ' To be sure you are getting at least two of a kind, you must select all of the other types of apples, plus two more. Meaning that only once you have selected all of the other apples can you be sure that you will select two of the kind you desire. It can be written like this: x,a x2, b and x3, c, with x representing the quantity of apples. This can be calculated by x2 + x3 +2. X2 representing one of the types of apples, x3 representing the other type and 2 representing 2 of the kind of apples you are trying to select. This is the only way to be sure you are getting at least two of a kind. ' '

7. Suppose you have 40 blue socks and 40 brown socks in a drawer. How many socks must you take from the drawer (without looking) to be sure of getting (i) a pair of the same colour, and (ii) a pair with different colors.

' 'You must take three socks from the drawer to ensure you have a pair that match. This is because if you only select two, one could be brown and one could be blue. Selecting three, ensures that at least two of them will be the same colour. As for part two, you would need to select 41 socks to ensure you had a pair of different coloured socks because if you select 40 or less you could get all the same colour, but selecting 41 ensures you will have at least one pair of mixed colour. ' '

8. Rueben says "Two days ago I was 20 years old. Later next year I will be 23 years old." Explain how this is possible.

' 'It is possible if your birthday is on the 31st of December and today is the 1st of January. This is because on the 30th of December (two days ago) you we’re 20 years old and now you are 21, later this year you will turn 22 on the 31st of December, and therefore 23 the next year.' '

9. A rope ladder hanging over the side of a boat has rungs one foot apart. Ten rungs are showing. If the tide rises five feet, how many rungs will be showing?

' ' 5 rungs will be showing, because if there are 10 showing now, and they are each a foot apart, then for 5 more rungs to be showing there would need to be an increase in the level of water by 5 feet. ' '

10.Suppose one-half of all people are chocolate eaters and one-half of all people are women. (i) Does it follow that one-fourth of all people are women chocolate eaters? (ii) Does it follow that one-half of all men are chocolate eaters? Explain.

' ' No, it does not follow that one-fourth of all people are women chocolate eaters and it does not follow that half of all men are chocolate eaters because are completely independent scenarios. Meaning that the the amount of women there are does not influence the amount of men that will eat chocolate. For example, If 50% of people are women and 50% of the entire population including men and women eat chocolate (arrived at by using the same logic that if 1/4 of women eat chocolate and 1/4 of men eat chocolate), that entire 50% could be comprised of women, meaning that no men eat chocolate disproving the statement.

11-14

Sifat Hasan

11. A woman, her older brother, her son, and her daughter are chess players. The worst player’s twin, who is one of the four players, and the best player are of opposite sex. The worst player and the best player have the same age. If this is possible, who is the worst player?

The four players (according to age, from oldest to youngest) are: woman's older brother, woman, and the son and the daughter (of the same age). Assuming that the children are of the same age (i.e. twins), the worst player is one of them, since they are the only ones who can have a twin. Assuming that the worst player is the daughter, her brother the son, is of the opposite sex as the woman, therefore the woman is the worst player. However, since the worst and the best player are of the same age, this is not possible, because the twins are of the opposite sex and they are of different genders.

12 A Manhattan fellow had a girlfriend in the Bronx and a girlfriend in Brooklyn. He decided which girlfriend to visit by arriving randomly at the train station and taking the first of the Bronx or Brooklyn trains that arrived. The trains to Brooklyn and the Bronx each arrived regularly every 10 minutes. Not long after he began his scheme the man's Bronx girlfriend left him because he rarely visited. Give a (logical) explanation

Assuming that the Bronx and the Brooklyn train arrive one after the other every 10 minutes, the only logical explanation would be that the man in Manhattan coincidentally went to the station 10 minutes or less before a train to Brooklyn arrived, most of the time.

==13 If a clock takes 5 seconds to strike 5:00 (with 5 equally spaced chimes), how long does it take to strike 10:00 (with 10 equally spaced chimes)?==

If it takes 5 seconds to strike 5, there will be 4 little halts in the middle. Therefore it takes 5 chimes 4 (5/4) = 1.25 second halts to finish. For 10 chimes, there are 9 halts so, it takes 9x 1.25 = 11.25 seconds for 10 halts.

==14 One day in the maternity ward, the name tags for four girl babies became mixed up. (i) In how many different ways could two of the babies be tagged correctly and two of the babies be tagged incorrectly? (ii) In how many different ways could three of the babies be tagged correctly and one baby be tagged incorrectly?==

(i)and (ii) If we take the babies names as A,B,C and D. There are 6 different combinations of the mix up, that two babies' names can be correct and 2 can be wrong. Assuming the name tags for the babies A,B,C and D are in respective order, they are ABDC, ADCB, ACBD, DBCA, CBAD and BACD. All other combinations for example BCAD will have one correct and 3 incorrect, or all four of them correct, because if 3 are correct, the fourth one has to be correct.

==15-16==
==Roland Will==

==15. Alex says to you, “I'll bet you any amount of money that if I shuffle this deck of cards, there will always be as many red cards in the first half of the deck as there are black cards in the second half of the deck.” Should you accept his bet?==

Answer: No, you shouldn't assuming the deck has equal amounts of red and black cards as in a standard 52 card deck.
Solution: In a standard 52 card deck, half of the cards (26) are black and half are red. If you take 26 cards at random from the deck, x of them will be black and y of them will be red, and x+y=26. As there are 26 of each color in the deck, then x+?=26 for the black cards in the deck and ?+y=26 for the red cards in the deck. As x+y=26 in the first randomly selected 26 cards, then the value of black cards in the other half of the deck must equal y, and the value of red cards in the other half of the deck must equal x meaning that "there will always be as many red cards in the first half of the deck as there are black cards in the second half of the deck."

==16. Suppose that each daughter in your family has the same number of brothers as she has sisters, and each son in your family has twice as many sisters as he has brothers. How many sons and daughters are in the family?==

Answer:3 total, 2 sister and 1 brother
Solution: Since the daughters in the family each have as many brothers as sisters the amount of sisters, with x standing for the amount of brothers, is x+1. As each brother has twice as many sisters as brothers, the amount of sisters must equal 2(x-1) or 2x-2. To find the number of brother: x+1=2x+1, 1=x-2, 3=x, which means that their are 3 brothers and 4 sisters (x+1= the number of sisters and x=3). This makes sense because a sister would have an equal amount of brothers to sisters, 3 sisters and 3 brothers, if there were 4 sisters and 3 brothers total, and each brother would have 4 sisters and 3 brothers, which is twice the amount of brothers to sisters.

==17~21==
==Audrey Chen==

==17.The zero point on a bathroom scale is set incorrectly, but otherwise the scale is accurate. It shows 60 kg when Dan stands on the scale, 50 kg when Sarah stands on the scale, but 105 kg when Dan and Sarah both stand on the scale. Does the scale read too high or too low? Explain. ==

''The scale read too low, since Dan is shown as 60kg and Sarah is 50kg, suppose 60+50=110, 105-110=-5, so that means the scale is smaller than 0 in the beginning''

==18. Alice takes one-third of the pennies from a large jar. Then Bret takes one-third of the remaining pennies from the jar. Finally, Carla takes one-third of the remaining pennies from the jar, leaving 40 pennies in the jar. How many pennies were in the jar at the start? ==

''If the total pennies is "x", Alice take 1/3x, so it has 2/3x left after Alice took it, than Bret take 1/3 out, after Alice took it, which is 2/3x*1/3= 2/9x, so in the beginning they have x, after Alice took it, it has 2/3x left, and Bret took 2/9x, so after Bret took it, it becomes 2/3x-2/9x= 4/9x-2/9x=2/9x left in the jar. Than Carla take 1/3 of the rest, so she took 1/3 of rest which is 2/9x*1/3=3/27x, so Alice took 1/3x, Bret tool 2/9x, Carla took 3/27x, three of them totaly took 1/3x+2/9x+3/27x=18/27x, so there still has x-18/27x= 9/27x= 1/3 left, 1/3x=40pennies, so x=120 pennies, so it was having 120 pennies in the jar.

==19. One morning each member of Angela's family drank an eight-ounce cup of coffee and milk, with the (nonzero) amounts of coffee and milk varying from cup to cup. Angela drank a quarter of the total amount of milk and a sixth of the total amount of coffee. What is the least number of people in the family? ==

''If we let total milk is x, total coffee is y. Than 1/4x+1/6y=8, and because every cup is 8ounce, x+y is multiple by 8. So make it easier, we use 1/4x+1/6y=8 * 12 to both sides. than we will got 3x+2y=96, now we have 3x+2y=96 and x+y is multiple of 8, and the number that multiple by 8 is 8, 16, 24, 32... so 2x+2y= 16, 32, 48, 64, 80, 96, since 3x+2y=96, it can't be more than 96. It will only have 6 possible number, so if you take 3x+2y=96 substracting 2x+2y=16, 32, 48, 64, 80, 96 you can get 6 possible x, which are 80, 64, 48, 32, 16, and 0. Than put the number into 3x+2y=96, if you put 80 in, will get 20, which is bigger than 8, and also 64, 48. If we use 32, it will equal to 8, but that means we have 0 coffee, but coffee can't be 0, so there's only 16 and 0 left. Since Angela had 1/4 of total amount of milk, milk can't be 0. So we got 16ounce than 16*(1/4)=4, so that means she had 8-4=4 's coffee. So 4=1/6 coffee, than the total amount of coffee would be 4*6=24. than x=16 and y=24, 16+24=40 40/8ounce=5, so at least have 5 cups of drinks, so that means at least they have 5 members in Angela's family.''

==20.Of two clocks next to each other, one runs 5 min per hour fast and the other runs 5 min per hour slow. At midnight the clocks show the same time. At what time are they are one hour apart? ==

''Since one clock runs 5 min faster per hour, the other is 5 min slower, after clock runs an hour, two clocks will have 10 min different from each other. 60 min an hour. 60/10=6, so after 6 hours two clocks will having one hour apart, and that would be 6AM.''

==21.Sven placed exactly in the middle among all runners in a race. Dan was slower than Sven, in 10th place, and Lars was in 16th place. How many runners were in the race? ==

''There were 17 runners. Since lars was in 16th place, the runners at least have to be 16, than if Sven is placed exactly in the middle, it means it would have even number of runners. Because Dan is slower and he was at 10 place that tells us Seven has to be before 10th, and if there has 19 runners, Sven and Dan would be at the same place, so it should be 17 runners, than Sven would be at exactly in the middle which at 9th place.''

==22-25==

Roland Will

22. During a vacation, it rained on 13 days, but when it rained in the morning, the afternoon was sunny, and every rainy afternoon was preceded by a sunny morning. There were 11 sunny mornings and 12 sunny afternoons. How long was the vacation?

Answer: 18 days of vacation.

Solution: 13 of the days of vacation were half sunny and half rainy. As there were 23 sunny mornings and afternoons (11 sunny mornings+12 sunny afternoons = 23 sunny mornings and afternoons), 13 of those sunny afternoons or mornings were on half rainy days. This means there are 10 sunny half-days left over, which equal 5 sunny full days. The 5 sunny full days plus the 13 half sunny/rainy days equal 18 total days of vacation.

23. Suppose you overhear the following conversation: Paul: How old are your three children? Paula: The product of their ages is 36 and the sum of their ages is the same as today's date. Paul: That is not enough information. Paula: The oldest child also has red hair. If you were Paul could you determine the ages of Paula's children? Explain.

Answer: If I were Paul this might be possible, but since we don’t know the date that Paula said this, it is not possible for us to find out.

Solution: There are many different combinations of three numbers that can be multiplied and will produce 36. As we do not know the date that Paula said this, the only thing we can be sure of is that the sum of the ages is less than 31 because no month has more than 31 days. Unfortunately, only one set of ages (ages 1 year old, 1 year old and 36 years old) has a sum greater than 31, which leaves many possible combinations open as possible. For today’s date, the 13th, ages of 2, 2, and 9 would produce 36 and have a sum of 13, but, again, it is uncertain. If it were the first of the month, there would be no possible combinations that would produce 36 and sum 1.

24. Two candles of equal length were lit at the same time. One candle took 6 hr to burn out and the other candle took 3 hr to burn out. After how much time was one candle exactly twice as long as the other candle?

Answer: 2 hours.

Solution: The faster burning candle took half the time to burn as the slower burning candle (3 hours/ 6 hours = 1/2), meaning it burned twice as fast. This means that after 2/3 of the total burning time for the faster burning candle it will be 1/3 of its original height and at the slower burning candle will be at 2/3 of its original height and 1/3 is half of 2/3. Since the faster burning candle took 3 hours to burn, 2/3 of its total burning time is 2 hours.

25. Two candles of length L and L + 1 were lit at 6:00 and 4:30, respectively. At 8:30 they had the same length. The longer candle died at 10:30 and the shorter candle died at 10:00. Find L.

Answer: L=2.

Solution: The shorter candle lasted for 4 hours and the longer candle lasted for 6 hours. As 6 hours – 4 hours = 2 hours and 2 hours / 4 hours = 1/2, the longer candle lasted 50% longer and was, therefore, 50% longer in length. This means that the +1 in L+1 on the longer candle was 1/2 of L. 1/2L=1, so L=2*1, L=2.

Course:MATH110/Archive/2010-2011/003/Groups/Group 18

2010-11-12T05:25:14Z

RolandWill: /* 11 11. A woman, her older brother, her son, and her daughter are chess players. The worst player’s twin, who is one of the four players, and the best player are of opposite sex. The worst player and the best player have the same age. If this is

{{Infobox MATH110 Groups
| group number = 18
| member 1 = [[User:ChouJuChen|Audrey Chen]]
| member 2 = [[User:SifatHasan|Sifat Hasan]]
| member 3 = [[User:CaitlinLastiwkaFarquharson|Caitlin Lastiwka-Farquharson]]
| member 4 = [[User:VictoriaWall|Victoria Wall]]
| member 5 = [[User:RolandWill|Roland Will]]
| member 6 =
}}

==Sub-Pages==

Basic Skills Project [http://wiki.ubc.ca/Course:MATH110/003/Groups/Group_18/Basic_Skills_Project]

==Homework due October 20th, 2010==

I created a page for our homework due tomorrow: [http://wiki.ubc.ca/Course:MATH110/003/Groups/Group_18/Homework_October_20th,_2010 http://wiki.ubc.ca/Course:MATH110/003/Groups/Group 18/Homework October 20th, 2010]

-Roland

I've moved the page, it was missing the ''Course:'' part which means it was created directly inside the wiki and not as a subpage of your group page, which is something the wiki admins don't like that much. By the way, you're allowed to use spaces in the name of your pages.

-- [[User:DavidKohler|DavidKohler]] 06:28, 20 October 2010 (UTC)

1-5

Victoria Wall

1.A bus traveled from the terminal to the airport at an average speed of 30 mi/hr and the trip took an hour and 20 min. The bus then traveled from the airport back to the terminal and again averaged 30 mi/hr. However, the return trip required 80 min. Explain.

' 'Lets call the terminal T and the airport A. If the bus travelled from T to A at 30mi/hr and it took them one hour and 20 mins to get from T to A at this speed, and there are 60 minutes in one hour, it took the bus 60min + 20min to get to A which is a total of 80min. The bus took 80 min to get from T to A. To get from A to T at the same speed (30mi/hr) it took the bus 80min. 80min = 80 min. This means going from A to T or vis versa at 30 mi/hr it will take the bus 80min.

2.A lady did not have her driver's license with her when she failed to stop at a stop sign and then went three blocks down a one-way street the wrong way. A policeman saw her, but he did not stop her. Explain.

' 'The lady was walking. It never says she was driving.

3.One of three boxes contains apples, another box contains oranges, and another box contains a mixture of apples and oranges. The boxes are labeled APPLES, ORANGES and APPLES AND ORANGES, but each label is incorrect. Can you select one fruit from only one box and determine the correct labels? Explain.

' 'if you selecet from the box APPLES AND ORANGES then you will be able to see the labels if they are correct or not.

4.I am the brother of the blind fiddler, but brothers I have none. How can this be?

' 'Since it says that he is the brother of the blind fiddler it does not mean that the fiddle is male, since he has no brothers than the fiddler must be a female.

5.Two quarters rest next to each other on a table. One coin is held fixed while the second coin is rolled around the edge of the first coin with no slipping. When the moving coin returns to its original position, how many times has it revolved?

' 'This is because the moving quarters revolves two full revolutions

6-10

Caitlin Lastiwka- Farquharson

6. Three kinds of apples are all mixed up in a basket. How many apples must you draw without (without looking) from the basket to be sure of getting at least two of a kind?

' ' To be sure you are getting at least two of a kind, you must select all of the other types of apples, plus two more. Meaning that only once you have selected all of the other apples can you be sure that you will select two of the kind you desire. It can be written like this: x,a x2, b and x3, c, with x representing the quantity of apples. This can be calculated by x2 + x3 +2. X2 representing one of the types of apples, x3 representing the other type and 2 representing 2 of the kind of apples you are trying to select. This is the only way to be sure you are getting at least two of a kind. ' '

7. Suppose you have 40 blue socks and 40 brown socks in a drawer. How many socks must you take from the drawer (without looking) to be sure of getting (i) a pair of the same colour, and (ii) a pair with different colors.

' 'You must take three socks from the drawer to ensure you have a pair that match. This is because if you only select two, one could be brown and one could be blue. Selecting three, ensures that at least two of them will be the same colour. As for part two, you would need to select 41 socks to ensure you had a pair of different coloured socks because if you select 40 or less you could get all the same colour, but selecting 41 ensures you will have at least one pair of mixed colour. ' '

8. Rueben says "Two days ago I was 20 years old. Later next year I will be 23 years old." Explain how this is possible.

' 'It is possible if your birthday is on the 31st of December and today is the 1st of January. This is because on the 30th of December (two days ago) you we’re 20 years old and now you are 21, later this year you will turn 22 on the 31st of December, and therefore 23 the next year.' '

9. A rope ladder hanging over the side of a boat has rungs one foot apart. Ten rungs are showing. If the tide rises five feet, how many rungs will be showing?

' ' 5 rungs will be showing, because if there are 10 showing now, and they are each a foot apart, then for 5 more rungs to be showing there would need to be an increase in the level of water by 5 feet. ' '

10.Suppose one-half of all people are chocolate eaters and one-half of all people are women. (i) Does it follow that one-fourth of all people are women chocolate eaters? (ii) Does it follow that one-half of all men are chocolate eaters? Explain.

' ' No, it does not follow that one-fourth of all people are women chocolate eaters and it does not follow that half of all men are chocolate eaters because are completely independent scenarios. Meaning that the the amount of women there are does not influence the amount of men that will eat chocolate. For example, If 50% of people are women and 50% of the entire population including men and women eat chocolate (arrived at by using the same logic that if 1/4 of women eat chocolate and 1/4 of men eat chocolate), that entire 50% could be comprised of women, meaning that no men eat chocolate disproving the statement.

11-14

Sifat Hasan

11. A woman, her older brother, her son, and her daughter are chess players. The worst player’s twin, who is one of the four players, and the best player are of opposite sex. The worst player and the best player have the same age. If this is possible, who is the worst player?

The four players (according to age, from oldest to youngest) are: woman's older brother, woman, and the son and the daughter (of the same age). Assuming that the children are of the same age (i.e. twins), the worst player is one of them, since they are the only ones who can have a twin. Assuming that the worst player is the daughter, her brother the son, is of the opposite sex as the woman, therefore the woman is the worst player. However, since the worst and the best player are of the same age, this is not possible, because the twins are of the opposite sex and they are of different genders.

==12 A Manhattan fellow had a girlfriend in the Bronx and a girlfriend in Brooklyn. He decided which girlfriend to visit by arriving randomly at the train station and taking the first of the Bronx or Brooklyn trains that arrived. The trains to Brooklyn and the Bronx each arrived regularly every 10 minutes. Not long after he began his scheme the man's Bronx girlfriend left him because he rarely visited. Give a (logical) explanation==

Assuming that the Bronx and the Brooklyn train arrive one after the other every 10 minutes, the only logical explanation would be that the man in Manhattan coincidentally went to the station 10 minutes or less before a train to Brooklyn arrived, most of the time.

==13 If a clock takes 5 seconds to strike 5:00 (with 5 equally spaced chimes), how long does it take to strike 10:00 (with 10 equally spaced chimes)?==

If it takes 5 seconds to strike 5, there will be 4 little halts in the middle. Therefore it takes 5 chimes 4 (5/4) = 1.25 second halts to finish. For 10 chimes, there are 9 halts so, it takes 9x 1.25 = 11.25 seconds for 10 halts.

==14 One day in the maternity ward, the name tags for four girl babies became mixed up. (i) In how many different ways could two of the babies be tagged correctly and two of the babies be tagged incorrectly? (ii) In how many different ways could three of the babies be tagged correctly and one baby be tagged incorrectly?==

(i)and (ii) If we take the babies names as A,B,C and D. There are 6 different combinations of the mix up, that two babies' names can be correct and 2 can be wrong. Assuming the name tags for the babies A,B,C and D are in respective order, they are ABDC, ADCB, ACBD, DBCA, CBAD and BACD. All other combinations for example BCAD will have one correct and 3 incorrect, or all four of them correct, because if 3 are correct, the fourth one has to be correct.

==15-16==
==Roland Will==

==15. Alex says to you, “I'll bet you any amount of money that if I shuffle this deck of cards, there will always be as many red cards in the first half of the deck as there are black cards in the second half of the deck.” Should you accept his bet?==

Answer: No, you shouldn't assuming the deck has equal amounts of red and black cards as in a standard 52 card deck.
Solution: In a standard 52 card deck, half of the cards (26) are black and half are red. If you take 26 cards at random from the deck, x of them will be black and y of them will be red, and x+y=26. As there are 26 of each color in the deck, then x+?=26 for the black cards in the deck and ?+y=26 for the red cards in the deck. As x+y=26 in the first randomly selected 26 cards, then the value of black cards in the other half of the deck must equal y, and the value of red cards in the other half of the deck must equal x meaning that "there will always be as many red cards in the first half of the deck as there are black cards in the second half of the deck."

==16. Suppose that each daughter in your family has the same number of brothers as she has sisters, and each son in your family has twice as many sisters as he has brothers. How many sons and daughters are in the family?==

Answer:3 total, 2 sister and 1 brother
Solution: Since the daughters in the family each have as many brothers as sisters the amount of sisters, with x standing for the amount of brothers, is x+1. As each brother has twice as many sisters as brothers, the amount of sisters must equal 2(x-1) or 2x-2. To find the number of brother: x+1=2x+1, 1=x-2, 3=x, which means that their are 3 brothers and 4 sisters (x+1= the number of sisters and x=3). This makes sense because a sister would have an equal amount of brothers to sisters, 3 sisters and 3 brothers, if there were 4 sisters and 3 brothers total, and each brother would have 4 sisters and 3 brothers, which is twice the amount of brothers to sisters.

==17~21==
==Audrey Chen==

==17.The zero point on a bathroom scale is set incorrectly, but otherwise the scale is accurate. It shows 60 kg when Dan stands on the scale, 50 kg when Sarah stands on the scale, but 105 kg when Dan and Sarah both stand on the scale. Does the scale read too high or too low? Explain. ==

''The scale read too low, since Dan is shown as 60kg and Sarah is 50kg, suppose 60+50=110, 105-110=-5, so that means the scale is smaller than 0 in the beginning''

==18. Alice takes one-third of the pennies from a large jar. Then Bret takes one-third of the remaining pennies from the jar. Finally, Carla takes one-third of the remaining pennies from the jar, leaving 40 pennies in the jar. How many pennies were in the jar at the start? ==

''If the total pennies is "x", Alice take 1/3x, so it has 2/3x left after Alice took it, than Bret take 1/3 out, after Alice took it, which is 2/3x*1/3= 2/9x, so in the beginning they have x, after Alice took it, it has 2/3x left, and Bret took 2/9x, so after Bret took it, it becomes 2/3x-2/9x= 4/9x-2/9x=2/9x left in the jar. Than Carla take 1/3 of the rest, so she took 1/3 of rest which is 2/9x*1/3=3/27x, so Alice took 1/3x, Bret tool 2/9x, Carla took 3/27x, three of them totaly took 1/3x+2/9x+3/27x=18/27x, so there still has x-18/27x= 9/27x= 1/3 left, 1/3x=40pennies, so x=120 pennies, so it was having 120 pennies in the jar.

==19. One morning each member of Angela's family drank an eight-ounce cup of coffee and milk, with the (nonzero) amounts of coffee and milk varying from cup to cup. Angela drank a quarter of the total amount of milk and a sixth of the total amount of coffee. What is the least number of people in the family? ==

''If we let total milk is x, total coffee is y. Than 1/4x+1/6y=8, and because every cup is 8ounce, x+y is multiple by 8. So make it easier, we use 1/4x+1/6y=8 * 12 to both sides. than we will got 3x+2y=96, now we have 3x+2y=96 and x+y is multiple of 8, and the number that multiple by 8 is 8, 16, 24, 32... so 2x+2y= 16, 32, 48, 64, 80, 96, since 3x+2y=96, it can't be more than 96. It will only have 6 possible number, so if you take 3x+2y=96 substracting 2x+2y=16, 32, 48, 64, 80, 96 you can get 6 possible x, which are 80, 64, 48, 32, 16, and 0. Than put the number into 3x+2y=96, if you put 80 in, will get 20, which is bigger than 8, and also 64, 48. If we use 32, it will equal to 8, but that means we have 0 coffee, but coffee can't be 0, so there's only 16 and 0 left. Since Angela had 1/4 of total amount of milk, milk can't be 0. So we got 16ounce than 16*(1/4)=4, so that means she had 8-4=4 's coffee. So 4=1/6 coffee, than the total amount of coffee would be 4*6=24. than x=16 and y=24, 16+24=40 40/8ounce=5, so at least have 5 cups of drinks, so that means at least they have 5 members in Angela's family.''

==20.Of two clocks next to each other, one runs 5 min per hour fast and the other runs 5 min per hour slow. At midnight the clocks show the same time. At what time are they are one hour apart? ==

''Since one clock runs 5 min faster per hour, the other is 5 min slower, after clock runs an hour, two clocks will have 10 min different from each other. 60 min an hour. 60/10=6, so after 6 hours two clocks will having one hour apart, and that would be 6AM.''

==21.Sven placed exactly in the middle among all runners in a race. Dan was slower than Sven, in 10th place, and Lars was in 16th place. How many runners were in the race? ==

''There were 17 runners. Since lars was in 16th place, the runners at least have to be 16, than if Sven is placed exactly in the middle, it means it would have even number of runners. Because Dan is slower and he was at 10 place that tells us Seven has to be before 10th, and if there has 19 runners, Sven and Dan would be at the same place, so it should be 17 runners, than Sven would be at exactly in the middle which at 9th place.''

==22-25==

Roland Will

22. During a vacation, it rained on 13 days, but when it rained in the morning, the afternoon was sunny, and every rainy afternoon was preceded by a sunny morning. There were 11 sunny mornings and 12 sunny afternoons. How long was the vacation?

Answer: 18 days of vacation.

Solution: 13 of the days of vacation were half sunny and half rainy. As there were 23 sunny mornings and afternoons (11 sunny mornings+12 sunny afternoons = 23 sunny mornings and afternoons), 13 of those sunny afternoons or mornings were on half rainy days. This means there are 10 sunny half-days left over, which equal 5 sunny full days. The 5 sunny full days plus the 13 half sunny/rainy days equal 18 total days of vacation.

23. Suppose you overhear the following conversation: Paul: How old are your three children? Paula: The product of their ages is 36 and the sum of their ages is the same as today's date. Paul: That is not enough information. Paula: The oldest child also has red hair. If you were Paul could you determine the ages of Paula's children? Explain.

Answer: If I were Paul this might be possible, but since we don’t know the date that Paula said this, it is not possible for us to find out.

Solution: There are many different combinations of three numbers that can be multiplied and will produce 36. As we do not know the date that Paula said this, the only thing we can be sure of is that the sum of the ages is less than 31 because no month has more than 31 days. Unfortunately, only one set of ages (ages 1 year old, 1 year old and 36 years old) has a sum greater than 31, which leaves many possible combinations open as possible. For today’s date, the 13th, ages of 2, 2, and 9 would produce 36 and have a sum of 13, but, again, it is uncertain. If it were the first of the month, there would be no possible combinations that would produce 36 and sum 1.

24. Two candles of equal length were lit at the same time. One candle took 6 hr to burn out and the other candle took 3 hr to burn out. After how much time was one candle exactly twice as long as the other candle?

Answer: 2 hours.

Solution: The faster burning candle took half the time to burn as the slower burning candle (3 hours/ 6 hours = 1/2), meaning it burned twice as fast. This means that after 2/3 of the total burning time for the faster burning candle it will be 1/3 of its original height and at the slower burning candle will be at 2/3 of its original height and 1/3 is half of 2/3. Since the faster burning candle took 3 hours to burn, 2/3 of its total burning time is 2 hours.

25. Two candles of length L and L + 1 were lit at 6:00 and 4:30, respectively. At 8:30 they had the same length. The longer candle died at 10:30 and the shorter candle died at 10:00. Find L.

Answer: L=2.

Solution: The shorter candle lasted for 4 hours and the longer candle lasted for 6 hours. As 6 hours – 4 hours = 2 hours and 2 hours / 4 hours = 1/2, the longer candle lasted 50% longer and was, therefore, 50% longer in length. This means that the +1 in L+1 on the longer candle was 1/2 of L. 1/2L=1, so L=2*1, L=2.

Course:MATH110/Archive/2010-2011/003/Groups/Group 18

2010-11-12T05:24:57Z

RolandWill: /* Sifat Hasan */

{{Infobox MATH110 Groups
| group number = 18
| member 1 = [[User:ChouJuChen|Audrey Chen]]
| member 2 = [[User:SifatHasan|Sifat Hasan]]
| member 3 = [[User:CaitlinLastiwkaFarquharson|Caitlin Lastiwka-Farquharson]]
| member 4 = [[User:VictoriaWall|Victoria Wall]]
| member 5 = [[User:RolandWill|Roland Will]]
| member 6 =
}}

==Sub-Pages==

Basic Skills Project [http://wiki.ubc.ca/Course:MATH110/003/Groups/Group_18/Basic_Skills_Project]

==Homework due October 20th, 2010==

I created a page for our homework due tomorrow: [http://wiki.ubc.ca/Course:MATH110/003/Groups/Group_18/Homework_October_20th,_2010 http://wiki.ubc.ca/Course:MATH110/003/Groups/Group 18/Homework October 20th, 2010]

-Roland

I've moved the page, it was missing the ''Course:'' part which means it was created directly inside the wiki and not as a subpage of your group page, which is something the wiki admins don't like that much. By the way, you're allowed to use spaces in the name of your pages.

-- [[User:DavidKohler|DavidKohler]] 06:28, 20 October 2010 (UTC)

1-5

Victoria Wall

1.A bus traveled from the terminal to the airport at an average speed of 30 mi/hr and the trip took an hour and 20 min. The bus then traveled from the airport back to the terminal and again averaged 30 mi/hr. However, the return trip required 80 min. Explain.

' 'Lets call the terminal T and the airport A. If the bus travelled from T to A at 30mi/hr and it took them one hour and 20 mins to get from T to A at this speed, and there are 60 minutes in one hour, it took the bus 60min + 20min to get to A which is a total of 80min. The bus took 80 min to get from T to A. To get from A to T at the same speed (30mi/hr) it took the bus 80min. 80min = 80 min. This means going from A to T or vis versa at 30 mi/hr it will take the bus 80min.

2.A lady did not have her driver's license with her when she failed to stop at a stop sign and then went three blocks down a one-way street the wrong way. A policeman saw her, but he did not stop her. Explain.

' 'The lady was walking. It never says she was driving.

3.One of three boxes contains apples, another box contains oranges, and another box contains a mixture of apples and oranges. The boxes are labeled APPLES, ORANGES and APPLES AND ORANGES, but each label is incorrect. Can you select one fruit from only one box and determine the correct labels? Explain.

' 'if you selecet from the box APPLES AND ORANGES then you will be able to see the labels if they are correct or not.

4.I am the brother of the blind fiddler, but brothers I have none. How can this be?

' 'Since it says that he is the brother of the blind fiddler it does not mean that the fiddle is male, since he has no brothers than the fiddler must be a female.

5.Two quarters rest next to each other on a table. One coin is held fixed while the second coin is rolled around the edge of the first coin with no slipping. When the moving coin returns to its original position, how many times has it revolved?

' 'This is because the moving quarters revolves two full revolutions

6-10

Caitlin Lastiwka- Farquharson

6. Three kinds of apples are all mixed up in a basket. How many apples must you draw without (without looking) from the basket to be sure of getting at least two of a kind?

' ' To be sure you are getting at least two of a kind, you must select all of the other types of apples, plus two more. Meaning that only once you have selected all of the other apples can you be sure that you will select two of the kind you desire. It can be written like this: x,a x2, b and x3, c, with x representing the quantity of apples. This can be calculated by x2 + x3 +2. X2 representing one of the types of apples, x3 representing the other type and 2 representing 2 of the kind of apples you are trying to select. This is the only way to be sure you are getting at least two of a kind. ' '

7. Suppose you have 40 blue socks and 40 brown socks in a drawer. How many socks must you take from the drawer (without looking) to be sure of getting (i) a pair of the same colour, and (ii) a pair with different colors.

' 'You must take three socks from the drawer to ensure you have a pair that match. This is because if you only select two, one could be brown and one could be blue. Selecting three, ensures that at least two of them will be the same colour. As for part two, you would need to select 41 socks to ensure you had a pair of different coloured socks because if you select 40 or less you could get all the same colour, but selecting 41 ensures you will have at least one pair of mixed colour. ' '

8. Rueben says "Two days ago I was 20 years old. Later next year I will be 23 years old." Explain how this is possible.

' 'It is possible if your birthday is on the 31st of December and today is the 1st of January. This is because on the 30th of December (two days ago) you we’re 20 years old and now you are 21, later this year you will turn 22 on the 31st of December, and therefore 23 the next year.' '

9. A rope ladder hanging over the side of a boat has rungs one foot apart. Ten rungs are showing. If the tide rises five feet, how many rungs will be showing?

' ' 5 rungs will be showing, because if there are 10 showing now, and they are each a foot apart, then for 5 more rungs to be showing there would need to be an increase in the level of water by 5 feet. ' '

10.Suppose one-half of all people are chocolate eaters and one-half of all people are women. (i) Does it follow that one-fourth of all people are women chocolate eaters? (ii) Does it follow that one-half of all men are chocolate eaters? Explain.

' ' No, it does not follow that one-fourth of all people are women chocolate eaters and it does not follow that half of all men are chocolate eaters because are completely independent scenarios. Meaning that the the amount of women there are does not influence the amount of men that will eat chocolate. For example, If 50% of people are women and 50% of the entire population including men and women eat chocolate (arrived at by using the same logic that if 1/4 of women eat chocolate and 1/4 of men eat chocolate), that entire 50% could be comprised of women, meaning that no men eat chocolate disproving the statement.

11-14

Sifat Hasan

==11 11. A woman, her older brother, her son, and her daughter are chess players. The worst player’s twin, who is one of the four players, and the best player are of opposite sex. The worst player and the best player have the same age. If this is possible, who is the worst player?==

The four players (according to age, from oldest to youngest) are: woman's older brother, woman, and the son and the daughter (of the same age). Assuming that the children are of the same age (i.e. twins), the worst player is one of them, since they are the only ones who can have a twin. Assuming that the worst player is the daughter, her brother the son, is of the opposite sex as the woman, therefore the woman is the worst player. However, since the worst and the best player are of the same age, this is not possible, because the twins are of the opposite sex and they are of different genders.

==12 A Manhattan fellow had a girlfriend in the Bronx and a girlfriend in Brooklyn. He decided which girlfriend to visit by arriving randomly at the train station and taking the first of the Bronx or Brooklyn trains that arrived. The trains to Brooklyn and the Bronx each arrived regularly every 10 minutes. Not long after he began his scheme the man's Bronx girlfriend left him because he rarely visited. Give a (logical) explanation==

Assuming that the Bronx and the Brooklyn train arrive one after the other every 10 minutes, the only logical explanation would be that the man in Manhattan coincidentally went to the station 10 minutes or less before a train to Brooklyn arrived, most of the time.

==13 If a clock takes 5 seconds to strike 5:00 (with 5 equally spaced chimes), how long does it take to strike 10:00 (with 10 equally spaced chimes)?==

If it takes 5 seconds to strike 5, there will be 4 little halts in the middle. Therefore it takes 5 chimes 4 (5/4) = 1.25 second halts to finish. For 10 chimes, there are 9 halts so, it takes 9x 1.25 = 11.25 seconds for 10 halts.

==14 One day in the maternity ward, the name tags for four girl babies became mixed up. (i) In how many different ways could two of the babies be tagged correctly and two of the babies be tagged incorrectly? (ii) In how many different ways could three of the babies be tagged correctly and one baby be tagged incorrectly?==

(i)and (ii) If we take the babies names as A,B,C and D. There are 6 different combinations of the mix up, that two babies' names can be correct and 2 can be wrong. Assuming the name tags for the babies A,B,C and D are in respective order, they are ABDC, ADCB, ACBD, DBCA, CBAD and BACD. All other combinations for example BCAD will have one correct and 3 incorrect, or all four of them correct, because if 3 are correct, the fourth one has to be correct.

==15-16==
==Roland Will==

==15. Alex says to you, “I'll bet you any amount of money that if I shuffle this deck of cards, there will always be as many red cards in the first half of the deck as there are black cards in the second half of the deck.” Should you accept his bet?==

Answer: No, you shouldn't assuming the deck has equal amounts of red and black cards as in a standard 52 card deck.
Solution: In a standard 52 card deck, half of the cards (26) are black and half are red. If you take 26 cards at random from the deck, x of them will be black and y of them will be red, and x+y=26. As there are 26 of each color in the deck, then x+?=26 for the black cards in the deck and ?+y=26 for the red cards in the deck. As x+y=26 in the first randomly selected 26 cards, then the value of black cards in the other half of the deck must equal y, and the value of red cards in the other half of the deck must equal x meaning that "there will always be as many red cards in the first half of the deck as there are black cards in the second half of the deck."

==16. Suppose that each daughter in your family has the same number of brothers as she has sisters, and each son in your family has twice as many sisters as he has brothers. How many sons and daughters are in the family?==

Answer:3 total, 2 sister and 1 brother
Solution: Since the daughters in the family each have as many brothers as sisters the amount of sisters, with x standing for the amount of brothers, is x+1. As each brother has twice as many sisters as brothers, the amount of sisters must equal 2(x-1) or 2x-2. To find the number of brother: x+1=2x+1, 1=x-2, 3=x, which means that their are 3 brothers and 4 sisters (x+1= the number of sisters and x=3). This makes sense because a sister would have an equal amount of brothers to sisters, 3 sisters and 3 brothers, if there were 4 sisters and 3 brothers total, and each brother would have 4 sisters and 3 brothers, which is twice the amount of brothers to sisters.

==17~21==
==Audrey Chen==

==17.The zero point on a bathroom scale is set incorrectly, but otherwise the scale is accurate. It shows 60 kg when Dan stands on the scale, 50 kg when Sarah stands on the scale, but 105 kg when Dan and Sarah both stand on the scale. Does the scale read too high or too low? Explain. ==

''The scale read too low, since Dan is shown as 60kg and Sarah is 50kg, suppose 60+50=110, 105-110=-5, so that means the scale is smaller than 0 in the beginning''

==18. Alice takes one-third of the pennies from a large jar. Then Bret takes one-third of the remaining pennies from the jar. Finally, Carla takes one-third of the remaining pennies from the jar, leaving 40 pennies in the jar. How many pennies were in the jar at the start? ==

''If the total pennies is "x", Alice take 1/3x, so it has 2/3x left after Alice took it, than Bret take 1/3 out, after Alice took it, which is 2/3x*1/3= 2/9x, so in the beginning they have x, after Alice took it, it has 2/3x left, and Bret took 2/9x, so after Bret took it, it becomes 2/3x-2/9x= 4/9x-2/9x=2/9x left in the jar. Than Carla take 1/3 of the rest, so she took 1/3 of rest which is 2/9x*1/3=3/27x, so Alice took 1/3x, Bret tool 2/9x, Carla took 3/27x, three of them totaly took 1/3x+2/9x+3/27x=18/27x, so there still has x-18/27x= 9/27x= 1/3 left, 1/3x=40pennies, so x=120 pennies, so it was having 120 pennies in the jar.

==19. One morning each member of Angela's family drank an eight-ounce cup of coffee and milk, with the (nonzero) amounts of coffee and milk varying from cup to cup. Angela drank a quarter of the total amount of milk and a sixth of the total amount of coffee. What is the least number of people in the family? ==

''If we let total milk is x, total coffee is y. Than 1/4x+1/6y=8, and because every cup is 8ounce, x+y is multiple by 8. So make it easier, we use 1/4x+1/6y=8 * 12 to both sides. than we will got 3x+2y=96, now we have 3x+2y=96 and x+y is multiple of 8, and the number that multiple by 8 is 8, 16, 24, 32... so 2x+2y= 16, 32, 48, 64, 80, 96, since 3x+2y=96, it can't be more than 96. It will only have 6 possible number, so if you take 3x+2y=96 substracting 2x+2y=16, 32, 48, 64, 80, 96 you can get 6 possible x, which are 80, 64, 48, 32, 16, and 0. Than put the number into 3x+2y=96, if you put 80 in, will get 20, which is bigger than 8, and also 64, 48. If we use 32, it will equal to 8, but that means we have 0 coffee, but coffee can't be 0, so there's only 16 and 0 left. Since Angela had 1/4 of total amount of milk, milk can't be 0. So we got 16ounce than 16*(1/4)=4, so that means she had 8-4=4 's coffee. So 4=1/6 coffee, than the total amount of coffee would be 4*6=24. than x=16 and y=24, 16+24=40 40/8ounce=5, so at least have 5 cups of drinks, so that means at least they have 5 members in Angela's family.''

==20.Of two clocks next to each other, one runs 5 min per hour fast and the other runs 5 min per hour slow. At midnight the clocks show the same time. At what time are they are one hour apart? ==

''Since one clock runs 5 min faster per hour, the other is 5 min slower, after clock runs an hour, two clocks will have 10 min different from each other. 60 min an hour. 60/10=6, so after 6 hours two clocks will having one hour apart, and that would be 6AM.''

==21.Sven placed exactly in the middle among all runners in a race. Dan was slower than Sven, in 10th place, and Lars was in 16th place. How many runners were in the race? ==

''There were 17 runners. Since lars was in 16th place, the runners at least have to be 16, than if Sven is placed exactly in the middle, it means it would have even number of runners. Because Dan is slower and he was at 10 place that tells us Seven has to be before 10th, and if there has 19 runners, Sven and Dan would be at the same place, so it should be 17 runners, than Sven would be at exactly in the middle which at 9th place.''

==22-25==

Roland Will

22. During a vacation, it rained on 13 days, but when it rained in the morning, the afternoon was sunny, and every rainy afternoon was preceded by a sunny morning. There were 11 sunny mornings and 12 sunny afternoons. How long was the vacation?

Answer: 18 days of vacation.

Solution: 13 of the days of vacation were half sunny and half rainy. As there were 23 sunny mornings and afternoons (11 sunny mornings+12 sunny afternoons = 23 sunny mornings and afternoons), 13 of those sunny afternoons or mornings were on half rainy days. This means there are 10 sunny half-days left over, which equal 5 sunny full days. The 5 sunny full days plus the 13 half sunny/rainy days equal 18 total days of vacation.

23. Suppose you overhear the following conversation: Paul: How old are your three children? Paula: The product of their ages is 36 and the sum of their ages is the same as today's date. Paul: That is not enough information. Paula: The oldest child also has red hair. If you were Paul could you determine the ages of Paula's children? Explain.

Answer: If I were Paul this might be possible, but since we don’t know the date that Paula said this, it is not possible for us to find out.

Solution: There are many different combinations of three numbers that can be multiplied and will produce 36. As we do not know the date that Paula said this, the only thing we can be sure of is that the sum of the ages is less than 31 because no month has more than 31 days. Unfortunately, only one set of ages (ages 1 year old, 1 year old and 36 years old) has a sum greater than 31, which leaves many possible combinations open as possible. For today’s date, the 13th, ages of 2, 2, and 9 would produce 36 and have a sum of 13, but, again, it is uncertain. If it were the first of the month, there would be no possible combinations that would produce 36 and sum 1.

24. Two candles of equal length were lit at the same time. One candle took 6 hr to burn out and the other candle took 3 hr to burn out. After how much time was one candle exactly twice as long as the other candle?

Answer: 2 hours.

Solution: The faster burning candle took half the time to burn as the slower burning candle (3 hours/ 6 hours = 1/2), meaning it burned twice as fast. This means that after 2/3 of the total burning time for the faster burning candle it will be 1/3 of its original height and at the slower burning candle will be at 2/3 of its original height and 1/3 is half of 2/3. Since the faster burning candle took 3 hours to burn, 2/3 of its total burning time is 2 hours.

25. Two candles of length L and L + 1 were lit at 6:00 and 4:30, respectively. At 8:30 they had the same length. The longer candle died at 10:30 and the shorter candle died at 10:00. Find L.

Answer: L=2.

Solution: The shorter candle lasted for 4 hours and the longer candle lasted for 6 hours. As 6 hours – 4 hours = 2 hours and 2 hours / 4 hours = 1/2, the longer candle lasted 50% longer and was, therefore, 50% longer in length. This means that the +1 in L+1 on the longer candle was 1/2 of L. 1/2L=1, so L=2*1, L=2.

Course:MATH110/Archive/2010-2011/003/Groups/Group 18

2010-11-12T05:24:44Z

RolandWill: /* 11-14 */

{{Infobox MATH110 Groups
| group number = 18
| member 1 = [[User:ChouJuChen|Audrey Chen]]
| member 2 = [[User:SifatHasan|Sifat Hasan]]
| member 3 = [[User:CaitlinLastiwkaFarquharson|Caitlin Lastiwka-Farquharson]]
| member 4 = [[User:VictoriaWall|Victoria Wall]]
| member 5 = [[User:RolandWill|Roland Will]]
| member 6 =
}}

==Sub-Pages==

Basic Skills Project [http://wiki.ubc.ca/Course:MATH110/003/Groups/Group_18/Basic_Skills_Project]

==Homework due October 20th, 2010==

I created a page for our homework due tomorrow: [http://wiki.ubc.ca/Course:MATH110/003/Groups/Group_18/Homework_October_20th,_2010 http://wiki.ubc.ca/Course:MATH110/003/Groups/Group 18/Homework October 20th, 2010]

-Roland

I've moved the page, it was missing the ''Course:'' part which means it was created directly inside the wiki and not as a subpage of your group page, which is something the wiki admins don't like that much. By the way, you're allowed to use spaces in the name of your pages.

-- [[User:DavidKohler|DavidKohler]] 06:28, 20 October 2010 (UTC)

1-5

Victoria Wall

1.A bus traveled from the terminal to the airport at an average speed of 30 mi/hr and the trip took an hour and 20 min. The bus then traveled from the airport back to the terminal and again averaged 30 mi/hr. However, the return trip required 80 min. Explain.

' 'Lets call the terminal T and the airport A. If the bus travelled from T to A at 30mi/hr and it took them one hour and 20 mins to get from T to A at this speed, and there are 60 minutes in one hour, it took the bus 60min + 20min to get to A which is a total of 80min. The bus took 80 min to get from T to A. To get from A to T at the same speed (30mi/hr) it took the bus 80min. 80min = 80 min. This means going from A to T or vis versa at 30 mi/hr it will take the bus 80min.

2.A lady did not have her driver's license with her when she failed to stop at a stop sign and then went three blocks down a one-way street the wrong way. A policeman saw her, but he did not stop her. Explain.

' 'The lady was walking. It never says she was driving.

3.One of three boxes contains apples, another box contains oranges, and another box contains a mixture of apples and oranges. The boxes are labeled APPLES, ORANGES and APPLES AND ORANGES, but each label is incorrect. Can you select one fruit from only one box and determine the correct labels? Explain.

' 'if you selecet from the box APPLES AND ORANGES then you will be able to see the labels if they are correct or not.

4.I am the brother of the blind fiddler, but brothers I have none. How can this be?

' 'Since it says that he is the brother of the blind fiddler it does not mean that the fiddle is male, since he has no brothers than the fiddler must be a female.

5.Two quarters rest next to each other on a table. One coin is held fixed while the second coin is rolled around the edge of the first coin with no slipping. When the moving coin returns to its original position, how many times has it revolved?

' 'This is because the moving quarters revolves two full revolutions

6-10

Caitlin Lastiwka- Farquharson

6. Three kinds of apples are all mixed up in a basket. How many apples must you draw without (without looking) from the basket to be sure of getting at least two of a kind?

' ' To be sure you are getting at least two of a kind, you must select all of the other types of apples, plus two more. Meaning that only once you have selected all of the other apples can you be sure that you will select two of the kind you desire. It can be written like this: x,a x2, b and x3, c, with x representing the quantity of apples. This can be calculated by x2 + x3 +2. X2 representing one of the types of apples, x3 representing the other type and 2 representing 2 of the kind of apples you are trying to select. This is the only way to be sure you are getting at least two of a kind. ' '

7. Suppose you have 40 blue socks and 40 brown socks in a drawer. How many socks must you take from the drawer (without looking) to be sure of getting (i) a pair of the same colour, and (ii) a pair with different colors.

' 'You must take three socks from the drawer to ensure you have a pair that match. This is because if you only select two, one could be brown and one could be blue. Selecting three, ensures that at least two of them will be the same colour. As for part two, you would need to select 41 socks to ensure you had a pair of different coloured socks because if you select 40 or less you could get all the same colour, but selecting 41 ensures you will have at least one pair of mixed colour. ' '

8. Rueben says "Two days ago I was 20 years old. Later next year I will be 23 years old." Explain how this is possible.

' 'It is possible if your birthday is on the 31st of December and today is the 1st of January. This is because on the 30th of December (two days ago) you we’re 20 years old and now you are 21, later this year you will turn 22 on the 31st of December, and therefore 23 the next year.' '

9. A rope ladder hanging over the side of a boat has rungs one foot apart. Ten rungs are showing. If the tide rises five feet, how many rungs will be showing?

' ' 5 rungs will be showing, because if there are 10 showing now, and they are each a foot apart, then for 5 more rungs to be showing there would need to be an increase in the level of water by 5 feet. ' '

10.Suppose one-half of all people are chocolate eaters and one-half of all people are women. (i) Does it follow that one-fourth of all people are women chocolate eaters? (ii) Does it follow that one-half of all men are chocolate eaters? Explain.

' ' No, it does not follow that one-fourth of all people are women chocolate eaters and it does not follow that half of all men are chocolate eaters because are completely independent scenarios. Meaning that the the amount of women there are does not influence the amount of men that will eat chocolate. For example, If 50% of people are women and 50% of the entire population including men and women eat chocolate (arrived at by using the same logic that if 1/4 of women eat chocolate and 1/4 of men eat chocolate), that entire 50% could be comprised of women, meaning that no men eat chocolate disproving the statement.

11-14

==Sifat Hasan==

==11 11. A woman, her older brother, her son, and her daughter are chess players. The worst player’s twin, who is one of the four players, and the best player are of opposite sex. The worst player and the best player have the same age. If this is possible, who is the worst player?==

The four players (according to age, from oldest to youngest) are: woman's older brother, woman, and the son and the daughter (of the same age). Assuming that the children are of the same age (i.e. twins), the worst player is one of them, since they are the only ones who can have a twin. Assuming that the worst player is the daughter, her brother the son, is of the opposite sex as the woman, therefore the woman is the worst player. However, since the worst and the best player are of the same age, this is not possible, because the twins are of the opposite sex and they are of different genders.

==12 A Manhattan fellow had a girlfriend in the Bronx and a girlfriend in Brooklyn. He decided which girlfriend to visit by arriving randomly at the train station and taking the first of the Bronx or Brooklyn trains that arrived. The trains to Brooklyn and the Bronx each arrived regularly every 10 minutes. Not long after he began his scheme the man's Bronx girlfriend left him because he rarely visited. Give a (logical) explanation==

Assuming that the Bronx and the Brooklyn train arrive one after the other every 10 minutes, the only logical explanation would be that the man in Manhattan coincidentally went to the station 10 minutes or less before a train to Brooklyn arrived, most of the time.

==13 If a clock takes 5 seconds to strike 5:00 (with 5 equally spaced chimes), how long does it take to strike 10:00 (with 10 equally spaced chimes)?==

If it takes 5 seconds to strike 5, there will be 4 little halts in the middle. Therefore it takes 5 chimes 4 (5/4) = 1.25 second halts to finish. For 10 chimes, there are 9 halts so, it takes 9x 1.25 = 11.25 seconds for 10 halts.

==14 One day in the maternity ward, the name tags for four girl babies became mixed up. (i) In how many different ways could two of the babies be tagged correctly and two of the babies be tagged incorrectly? (ii) In how many different ways could three of the babies be tagged correctly and one baby be tagged incorrectly?==

(i)and (ii) If we take the babies names as A,B,C and D. There are 6 different combinations of the mix up, that two babies' names can be correct and 2 can be wrong. Assuming the name tags for the babies A,B,C and D are in respective order, they are ABDC, ADCB, ACBD, DBCA, CBAD and BACD. All other combinations for example BCAD will have one correct and 3 incorrect, or all four of them correct, because if 3 are correct, the fourth one has to be correct.

==15-16==
==Roland Will==

==15. Alex says to you, “I'll bet you any amount of money that if I shuffle this deck of cards, there will always be as many red cards in the first half of the deck as there are black cards in the second half of the deck.” Should you accept his bet?==

Answer: No, you shouldn't assuming the deck has equal amounts of red and black cards as in a standard 52 card deck.
Solution: In a standard 52 card deck, half of the cards (26) are black and half are red. If you take 26 cards at random from the deck, x of them will be black and y of them will be red, and x+y=26. As there are 26 of each color in the deck, then x+?=26 for the black cards in the deck and ?+y=26 for the red cards in the deck. As x+y=26 in the first randomly selected 26 cards, then the value of black cards in the other half of the deck must equal y, and the value of red cards in the other half of the deck must equal x meaning that "there will always be as many red cards in the first half of the deck as there are black cards in the second half of the deck."

==16. Suppose that each daughter in your family has the same number of brothers as she has sisters, and each son in your family has twice as many sisters as he has brothers. How many sons and daughters are in the family?==

Answer:3 total, 2 sister and 1 brother
Solution: Since the daughters in the family each have as many brothers as sisters the amount of sisters, with x standing for the amount of brothers, is x+1. As each brother has twice as many sisters as brothers, the amount of sisters must equal 2(x-1) or 2x-2. To find the number of brother: x+1=2x+1, 1=x-2, 3=x, which means that their are 3 brothers and 4 sisters (x+1= the number of sisters and x=3). This makes sense because a sister would have an equal amount of brothers to sisters, 3 sisters and 3 brothers, if there were 4 sisters and 3 brothers total, and each brother would have 4 sisters and 3 brothers, which is twice the amount of brothers to sisters.

==17~21==
==Audrey Chen==

==17.The zero point on a bathroom scale is set incorrectly, but otherwise the scale is accurate. It shows 60 kg when Dan stands on the scale, 50 kg when Sarah stands on the scale, but 105 kg when Dan and Sarah both stand on the scale. Does the scale read too high or too low? Explain. ==

''The scale read too low, since Dan is shown as 60kg and Sarah is 50kg, suppose 60+50=110, 105-110=-5, so that means the scale is smaller than 0 in the beginning''

==18. Alice takes one-third of the pennies from a large jar. Then Bret takes one-third of the remaining pennies from the jar. Finally, Carla takes one-third of the remaining pennies from the jar, leaving 40 pennies in the jar. How many pennies were in the jar at the start? ==

''If the total pennies is "x", Alice take 1/3x, so it has 2/3x left after Alice took it, than Bret take 1/3 out, after Alice took it, which is 2/3x*1/3= 2/9x, so in the beginning they have x, after Alice took it, it has 2/3x left, and Bret took 2/9x, so after Bret took it, it becomes 2/3x-2/9x= 4/9x-2/9x=2/9x left in the jar. Than Carla take 1/3 of the rest, so she took 1/3 of rest which is 2/9x*1/3=3/27x, so Alice took 1/3x, Bret tool 2/9x, Carla took 3/27x, three of them totaly took 1/3x+2/9x+3/27x=18/27x, so there still has x-18/27x= 9/27x= 1/3 left, 1/3x=40pennies, so x=120 pennies, so it was having 120 pennies in the jar.

==19. One morning each member of Angela's family drank an eight-ounce cup of coffee and milk, with the (nonzero) amounts of coffee and milk varying from cup to cup. Angela drank a quarter of the total amount of milk and a sixth of the total amount of coffee. What is the least number of people in the family? ==

''If we let total milk is x, total coffee is y. Than 1/4x+1/6y=8, and because every cup is 8ounce, x+y is multiple by 8. So make it easier, we use 1/4x+1/6y=8 * 12 to both sides. than we will got 3x+2y=96, now we have 3x+2y=96 and x+y is multiple of 8, and the number that multiple by 8 is 8, 16, 24, 32... so 2x+2y= 16, 32, 48, 64, 80, 96, since 3x+2y=96, it can't be more than 96. It will only have 6 possible number, so if you take 3x+2y=96 substracting 2x+2y=16, 32, 48, 64, 80, 96 you can get 6 possible x, which are 80, 64, 48, 32, 16, and 0. Than put the number into 3x+2y=96, if you put 80 in, will get 20, which is bigger than 8, and also 64, 48. If we use 32, it will equal to 8, but that means we have 0 coffee, but coffee can't be 0, so there's only 16 and 0 left. Since Angela had 1/4 of total amount of milk, milk can't be 0. So we got 16ounce than 16*(1/4)=4, so that means she had 8-4=4 's coffee. So 4=1/6 coffee, than the total amount of coffee would be 4*6=24. than x=16 and y=24, 16+24=40 40/8ounce=5, so at least have 5 cups of drinks, so that means at least they have 5 members in Angela's family.''

==20.Of two clocks next to each other, one runs 5 min per hour fast and the other runs 5 min per hour slow. At midnight the clocks show the same time. At what time are they are one hour apart? ==

''Since one clock runs 5 min faster per hour, the other is 5 min slower, after clock runs an hour, two clocks will have 10 min different from each other. 60 min an hour. 60/10=6, so after 6 hours two clocks will having one hour apart, and that would be 6AM.''

==21.Sven placed exactly in the middle among all runners in a race. Dan was slower than Sven, in 10th place, and Lars was in 16th place. How many runners were in the race? ==

''There were 17 runners. Since lars was in 16th place, the runners at least have to be 16, than if Sven is placed exactly in the middle, it means it would have even number of runners. Because Dan is slower and he was at 10 place that tells us Seven has to be before 10th, and if there has 19 runners, Sven and Dan would be at the same place, so it should be 17 runners, than Sven would be at exactly in the middle which at 9th place.''

==22-25==

Roland Will

22. During a vacation, it rained on 13 days, but when it rained in the morning, the afternoon was sunny, and every rainy afternoon was preceded by a sunny morning. There were 11 sunny mornings and 12 sunny afternoons. How long was the vacation?

Answer: 18 days of vacation.

Solution: 13 of the days of vacation were half sunny and half rainy. As there were 23 sunny mornings and afternoons (11 sunny mornings+12 sunny afternoons = 23 sunny mornings and afternoons), 13 of those sunny afternoons or mornings were on half rainy days. This means there are 10 sunny half-days left over, which equal 5 sunny full days. The 5 sunny full days plus the 13 half sunny/rainy days equal 18 total days of vacation.

23. Suppose you overhear the following conversation: Paul: How old are your three children? Paula: The product of their ages is 36 and the sum of their ages is the same as today's date. Paul: That is not enough information. Paula: The oldest child also has red hair. If you were Paul could you determine the ages of Paula's children? Explain.

Answer: If I were Paul this might be possible, but since we don’t know the date that Paula said this, it is not possible for us to find out.

Solution: There are many different combinations of three numbers that can be multiplied and will produce 36. As we do not know the date that Paula said this, the only thing we can be sure of is that the sum of the ages is less than 31 because no month has more than 31 days. Unfortunately, only one set of ages (ages 1 year old, 1 year old and 36 years old) has a sum greater than 31, which leaves many possible combinations open as possible. For today’s date, the 13th, ages of 2, 2, and 9 would produce 36 and have a sum of 13, but, again, it is uncertain. If it were the first of the month, there would be no possible combinations that would produce 36 and sum 1.

24. Two candles of equal length were lit at the same time. One candle took 6 hr to burn out and the other candle took 3 hr to burn out. After how much time was one candle exactly twice as long as the other candle?

Answer: 2 hours.

Solution: The faster burning candle took half the time to burn as the slower burning candle (3 hours/ 6 hours = 1/2), meaning it burned twice as fast. This means that after 2/3 of the total burning time for the faster burning candle it will be 1/3 of its original height and at the slower burning candle will be at 2/3 of its original height and 1/3 is half of 2/3. Since the faster burning candle took 3 hours to burn, 2/3 of its total burning time is 2 hours.

25. Two candles of length L and L + 1 were lit at 6:00 and 4:30, respectively. At 8:30 they had the same length. The longer candle died at 10:30 and the shorter candle died at 10:00. Find L.

Answer: L=2.

Solution: The shorter candle lasted for 4 hours and the longer candle lasted for 6 hours. As 6 hours – 4 hours = 2 hours and 2 hours / 4 hours = 1/2, the longer candle lasted 50% longer and was, therefore, 50% longer in length. This means that the +1 in L+1 on the longer candle was 1/2 of L. 1/2L=1, so L=2*1, L=2.

Course:MATH110/Archive/2010-2011/003/Groups/Group 18

2010-11-12T05:24:33Z

RolandWill: /* 10.Suppose one-half of all people are chocolate eaters and one-half of all people are women. (i) Does it follow that one-fourth of all people are women chocolate eaters? (ii) Does it follow that one-half of all men are chocolate eaters? Explain. *

{{Infobox MATH110 Groups
| group number = 18
| member 1 = [[User:ChouJuChen|Audrey Chen]]
| member 2 = [[User:SifatHasan|Sifat Hasan]]
| member 3 = [[User:CaitlinLastiwkaFarquharson|Caitlin Lastiwka-Farquharson]]
| member 4 = [[User:VictoriaWall|Victoria Wall]]
| member 5 = [[User:RolandWill|Roland Will]]
| member 6 =
}}

==Sub-Pages==

Basic Skills Project [http://wiki.ubc.ca/Course:MATH110/003/Groups/Group_18/Basic_Skills_Project]

==Homework due October 20th, 2010==

I created a page for our homework due tomorrow: [http://wiki.ubc.ca/Course:MATH110/003/Groups/Group_18/Homework_October_20th,_2010 http://wiki.ubc.ca/Course:MATH110/003/Groups/Group 18/Homework October 20th, 2010]

-Roland

I've moved the page, it was missing the ''Course:'' part which means it was created directly inside the wiki and not as a subpage of your group page, which is something the wiki admins don't like that much. By the way, you're allowed to use spaces in the name of your pages.

-- [[User:DavidKohler|DavidKohler]] 06:28, 20 October 2010 (UTC)

1-5

Victoria Wall

1.A bus traveled from the terminal to the airport at an average speed of 30 mi/hr and the trip took an hour and 20 min. The bus then traveled from the airport back to the terminal and again averaged 30 mi/hr. However, the return trip required 80 min. Explain.

' 'Lets call the terminal T and the airport A. If the bus travelled from T to A at 30mi/hr and it took them one hour and 20 mins to get from T to A at this speed, and there are 60 minutes in one hour, it took the bus 60min + 20min to get to A which is a total of 80min. The bus took 80 min to get from T to A. To get from A to T at the same speed (30mi/hr) it took the bus 80min. 80min = 80 min. This means going from A to T or vis versa at 30 mi/hr it will take the bus 80min.

2.A lady did not have her driver's license with her when she failed to stop at a stop sign and then went three blocks down a one-way street the wrong way. A policeman saw her, but he did not stop her. Explain.

' 'The lady was walking. It never says she was driving.

3.One of three boxes contains apples, another box contains oranges, and another box contains a mixture of apples and oranges. The boxes are labeled APPLES, ORANGES and APPLES AND ORANGES, but each label is incorrect. Can you select one fruit from only one box and determine the correct labels? Explain.

' 'if you selecet from the box APPLES AND ORANGES then you will be able to see the labels if they are correct or not.

4.I am the brother of the blind fiddler, but brothers I have none. How can this be?

' 'Since it says that he is the brother of the blind fiddler it does not mean that the fiddle is male, since he has no brothers than the fiddler must be a female.

5.Two quarters rest next to each other on a table. One coin is held fixed while the second coin is rolled around the edge of the first coin with no slipping. When the moving coin returns to its original position, how many times has it revolved?

' 'This is because the moving quarters revolves two full revolutions

6-10

Caitlin Lastiwka- Farquharson

6. Three kinds of apples are all mixed up in a basket. How many apples must you draw without (without looking) from the basket to be sure of getting at least two of a kind?

' ' To be sure you are getting at least two of a kind, you must select all of the other types of apples, plus two more. Meaning that only once you have selected all of the other apples can you be sure that you will select two of the kind you desire. It can be written like this: x,a x2, b and x3, c, with x representing the quantity of apples. This can be calculated by x2 + x3 +2. X2 representing one of the types of apples, x3 representing the other type and 2 representing 2 of the kind of apples you are trying to select. This is the only way to be sure you are getting at least two of a kind. ' '

7. Suppose you have 40 blue socks and 40 brown socks in a drawer. How many socks must you take from the drawer (without looking) to be sure of getting (i) a pair of the same colour, and (ii) a pair with different colors.

' 'You must take three socks from the drawer to ensure you have a pair that match. This is because if you only select two, one could be brown and one could be blue. Selecting three, ensures that at least two of them will be the same colour. As for part two, you would need to select 41 socks to ensure you had a pair of different coloured socks because if you select 40 or less you could get all the same colour, but selecting 41 ensures you will have at least one pair of mixed colour. ' '

8. Rueben says "Two days ago I was 20 years old. Later next year I will be 23 years old." Explain how this is possible.

' 'It is possible if your birthday is on the 31st of December and today is the 1st of January. This is because on the 30th of December (two days ago) you we’re 20 years old and now you are 21, later this year you will turn 22 on the 31st of December, and therefore 23 the next year.' '

9. A rope ladder hanging over the side of a boat has rungs one foot apart. Ten rungs are showing. If the tide rises five feet, how many rungs will be showing?

' ' 5 rungs will be showing, because if there are 10 showing now, and they are each a foot apart, then for 5 more rungs to be showing there would need to be an increase in the level of water by 5 feet. ' '

10.Suppose one-half of all people are chocolate eaters and one-half of all people are women. (i) Does it follow that one-fourth of all people are women chocolate eaters? (ii) Does it follow that one-half of all men are chocolate eaters? Explain.

' ' No, it does not follow that one-fourth of all people are women chocolate eaters and it does not follow that half of all men are chocolate eaters because are completely independent scenarios. Meaning that the the amount of women there are does not influence the amount of men that will eat chocolate. For example, If 50% of people are women and 50% of the entire population including men and women eat chocolate (arrived at by using the same logic that if 1/4 of women eat chocolate and 1/4 of men eat chocolate), that entire 50% could be comprised of women, meaning that no men eat chocolate disproving the statement.

==11-14==
==Sifat Hasan==

==11 11. A woman, her older brother, her son, and her daughter are chess players. The worst player’s twin, who is one of the four players, and the best player are of opposite sex. The worst player and the best player have the same age. If this is possible, who is the worst player?==

The four players (according to age, from oldest to youngest) are: woman's older brother, woman, and the son and the daughter (of the same age). Assuming that the children are of the same age (i.e. twins), the worst player is one of them, since they are the only ones who can have a twin. Assuming that the worst player is the daughter, her brother the son, is of the opposite sex as the woman, therefore the woman is the worst player. However, since the worst and the best player are of the same age, this is not possible, because the twins are of the opposite sex and they are of different genders.

==12 A Manhattan fellow had a girlfriend in the Bronx and a girlfriend in Brooklyn. He decided which girlfriend to visit by arriving randomly at the train station and taking the first of the Bronx or Brooklyn trains that arrived. The trains to Brooklyn and the Bronx each arrived regularly every 10 minutes. Not long after he began his scheme the man's Bronx girlfriend left him because he rarely visited. Give a (logical) explanation==

Assuming that the Bronx and the Brooklyn train arrive one after the other every 10 minutes, the only logical explanation would be that the man in Manhattan coincidentally went to the station 10 minutes or less before a train to Brooklyn arrived, most of the time.

==13 If a clock takes 5 seconds to strike 5:00 (with 5 equally spaced chimes), how long does it take to strike 10:00 (with 10 equally spaced chimes)?==

If it takes 5 seconds to strike 5, there will be 4 little halts in the middle. Therefore it takes 5 chimes 4 (5/4) = 1.25 second halts to finish. For 10 chimes, there are 9 halts so, it takes 9x 1.25 = 11.25 seconds for 10 halts.

==14 One day in the maternity ward, the name tags for four girl babies became mixed up. (i) In how many different ways could two of the babies be tagged correctly and two of the babies be tagged incorrectly? (ii) In how many different ways could three of the babies be tagged correctly and one baby be tagged incorrectly?==

(i)and (ii) If we take the babies names as A,B,C and D. There are 6 different combinations of the mix up, that two babies' names can be correct and 2 can be wrong. Assuming the name tags for the babies A,B,C and D are in respective order, they are ABDC, ADCB, ACBD, DBCA, CBAD and BACD. All other combinations for example BCAD will have one correct and 3 incorrect, or all four of them correct, because if 3 are correct, the fourth one has to be correct.

==15-16==
==Roland Will==

==15. Alex says to you, “I'll bet you any amount of money that if I shuffle this deck of cards, there will always be as many red cards in the first half of the deck as there are black cards in the second half of the deck.” Should you accept his bet?==

Answer: No, you shouldn't assuming the deck has equal amounts of red and black cards as in a standard 52 card deck.
Solution: In a standard 52 card deck, half of the cards (26) are black and half are red. If you take 26 cards at random from the deck, x of them will be black and y of them will be red, and x+y=26. As there are 26 of each color in the deck, then x+?=26 for the black cards in the deck and ?+y=26 for the red cards in the deck. As x+y=26 in the first randomly selected 26 cards, then the value of black cards in the other half of the deck must equal y, and the value of red cards in the other half of the deck must equal x meaning that "there will always be as many red cards in the first half of the deck as there are black cards in the second half of the deck."

==16. Suppose that each daughter in your family has the same number of brothers as she has sisters, and each son in your family has twice as many sisters as he has brothers. How many sons and daughters are in the family?==

Answer:3 total, 2 sister and 1 brother
Solution: Since the daughters in the family each have as many brothers as sisters the amount of sisters, with x standing for the amount of brothers, is x+1. As each brother has twice as many sisters as brothers, the amount of sisters must equal 2(x-1) or 2x-2. To find the number of brother: x+1=2x+1, 1=x-2, 3=x, which means that their are 3 brothers and 4 sisters (x+1= the number of sisters and x=3). This makes sense because a sister would have an equal amount of brothers to sisters, 3 sisters and 3 brothers, if there were 4 sisters and 3 brothers total, and each brother would have 4 sisters and 3 brothers, which is twice the amount of brothers to sisters.

==17~21==
==Audrey Chen==

==17.The zero point on a bathroom scale is set incorrectly, but otherwise the scale is accurate. It shows 60 kg when Dan stands on the scale, 50 kg when Sarah stands on the scale, but 105 kg when Dan and Sarah both stand on the scale. Does the scale read too high or too low? Explain. ==

''The scale read too low, since Dan is shown as 60kg and Sarah is 50kg, suppose 60+50=110, 105-110=-5, so that means the scale is smaller than 0 in the beginning''

==18. Alice takes one-third of the pennies from a large jar. Then Bret takes one-third of the remaining pennies from the jar. Finally, Carla takes one-third of the remaining pennies from the jar, leaving 40 pennies in the jar. How many pennies were in the jar at the start? ==

''If the total pennies is "x", Alice take 1/3x, so it has 2/3x left after Alice took it, than Bret take 1/3 out, after Alice took it, which is 2/3x*1/3= 2/9x, so in the beginning they have x, after Alice took it, it has 2/3x left, and Bret took 2/9x, so after Bret took it, it becomes 2/3x-2/9x= 4/9x-2/9x=2/9x left in the jar. Than Carla take 1/3 of the rest, so she took 1/3 of rest which is 2/9x*1/3=3/27x, so Alice took 1/3x, Bret tool 2/9x, Carla took 3/27x, three of them totaly took 1/3x+2/9x+3/27x=18/27x, so there still has x-18/27x= 9/27x= 1/3 left, 1/3x=40pennies, so x=120 pennies, so it was having 120 pennies in the jar.

==19. One morning each member of Angela's family drank an eight-ounce cup of coffee and milk, with the (nonzero) amounts of coffee and milk varying from cup to cup. Angela drank a quarter of the total amount of milk and a sixth of the total amount of coffee. What is the least number of people in the family? ==

''If we let total milk is x, total coffee is y. Than 1/4x+1/6y=8, and because every cup is 8ounce, x+y is multiple by 8. So make it easier, we use 1/4x+1/6y=8 * 12 to both sides. than we will got 3x+2y=96, now we have 3x+2y=96 and x+y is multiple of 8, and the number that multiple by 8 is 8, 16, 24, 32... so 2x+2y= 16, 32, 48, 64, 80, 96, since 3x+2y=96, it can't be more than 96. It will only have 6 possible number, so if you take 3x+2y=96 substracting 2x+2y=16, 32, 48, 64, 80, 96 you can get 6 possible x, which are 80, 64, 48, 32, 16, and 0. Than put the number into 3x+2y=96, if you put 80 in, will get 20, which is bigger than 8, and also 64, 48. If we use 32, it will equal to 8, but that means we have 0 coffee, but coffee can't be 0, so there's only 16 and 0 left. Since Angela had 1/4 of total amount of milk, milk can't be 0. So we got 16ounce than 16*(1/4)=4, so that means she had 8-4=4 's coffee. So 4=1/6 coffee, than the total amount of coffee would be 4*6=24. than x=16 and y=24, 16+24=40 40/8ounce=5, so at least have 5 cups of drinks, so that means at least they have 5 members in Angela's family.''

==20.Of two clocks next to each other, one runs 5 min per hour fast and the other runs 5 min per hour slow. At midnight the clocks show the same time. At what time are they are one hour apart? ==

''Since one clock runs 5 min faster per hour, the other is 5 min slower, after clock runs an hour, two clocks will have 10 min different from each other. 60 min an hour. 60/10=6, so after 6 hours two clocks will having one hour apart, and that would be 6AM.''

==21.Sven placed exactly in the middle among all runners in a race. Dan was slower than Sven, in 10th place, and Lars was in 16th place. How many runners were in the race? ==

''There were 17 runners. Since lars was in 16th place, the runners at least have to be 16, than if Sven is placed exactly in the middle, it means it would have even number of runners. Because Dan is slower and he was at 10 place that tells us Seven has to be before 10th, and if there has 19 runners, Sven and Dan would be at the same place, so it should be 17 runners, than Sven would be at exactly in the middle which at 9th place.''

==22-25==

Roland Will

22. During a vacation, it rained on 13 days, but when it rained in the morning, the afternoon was sunny, and every rainy afternoon was preceded by a sunny morning. There were 11 sunny mornings and 12 sunny afternoons. How long was the vacation?

Answer: 18 days of vacation.

Solution: 13 of the days of vacation were half sunny and half rainy. As there were 23 sunny mornings and afternoons (11 sunny mornings+12 sunny afternoons = 23 sunny mornings and afternoons), 13 of those sunny afternoons or mornings were on half rainy days. This means there are 10 sunny half-days left over, which equal 5 sunny full days. The 5 sunny full days plus the 13 half sunny/rainy days equal 18 total days of vacation.

23. Suppose you overhear the following conversation: Paul: How old are your three children? Paula: The product of their ages is 36 and the sum of their ages is the same as today's date. Paul: That is not enough information. Paula: The oldest child also has red hair. If you were Paul could you determine the ages of Paula's children? Explain.

Answer: If I were Paul this might be possible, but since we don’t know the date that Paula said this, it is not possible for us to find out.

Solution: There are many different combinations of three numbers that can be multiplied and will produce 36. As we do not know the date that Paula said this, the only thing we can be sure of is that the sum of the ages is less than 31 because no month has more than 31 days. Unfortunately, only one set of ages (ages 1 year old, 1 year old and 36 years old) has a sum greater than 31, which leaves many possible combinations open as possible. For today’s date, the 13th, ages of 2, 2, and 9 would produce 36 and have a sum of 13, but, again, it is uncertain. If it were the first of the month, there would be no possible combinations that would produce 36 and sum 1.

24. Two candles of equal length were lit at the same time. One candle took 6 hr to burn out and the other candle took 3 hr to burn out. After how much time was one candle exactly twice as long as the other candle?

Answer: 2 hours.

Solution: The faster burning candle took half the time to burn as the slower burning candle (3 hours/ 6 hours = 1/2), meaning it burned twice as fast. This means that after 2/3 of the total burning time for the faster burning candle it will be 1/3 of its original height and at the slower burning candle will be at 2/3 of its original height and 1/3 is half of 2/3. Since the faster burning candle took 3 hours to burn, 2/3 of its total burning time is 2 hours.

25. Two candles of length L and L + 1 were lit at 6:00 and 4:30, respectively. At 8:30 they had the same length. The longer candle died at 10:30 and the shorter candle died at 10:00. Find L.

Answer: L=2.

Solution: The shorter candle lasted for 4 hours and the longer candle lasted for 6 hours. As 6 hours – 4 hours = 2 hours and 2 hours / 4 hours = 1/2, the longer candle lasted 50% longer and was, therefore, 50% longer in length. This means that the +1 in L+1 on the longer candle was 1/2 of L. 1/2L=1, so L=2*1, L=2.

Course:MATH110/Archive/2010-2011/003/Groups/Group 18

2010-11-12T05:24:20Z

RolandWill: /* 9. A rope ladder hanging over the side of a boat has rungs one foot apart. Ten rungs are showing. If the tide rises five feet, how many rungs will be showing? */

{{Infobox MATH110 Groups
| group number = 18
| member 1 = [[User:ChouJuChen|Audrey Chen]]
| member 2 = [[User:SifatHasan|Sifat Hasan]]
| member 3 = [[User:CaitlinLastiwkaFarquharson|Caitlin Lastiwka-Farquharson]]
| member 4 = [[User:VictoriaWall|Victoria Wall]]
| member 5 = [[User:RolandWill|Roland Will]]
| member 6 =
}}

==Sub-Pages==

Basic Skills Project [http://wiki.ubc.ca/Course:MATH110/003/Groups/Group_18/Basic_Skills_Project]

==Homework due October 20th, 2010==

I created a page for our homework due tomorrow: [http://wiki.ubc.ca/Course:MATH110/003/Groups/Group_18/Homework_October_20th,_2010 http://wiki.ubc.ca/Course:MATH110/003/Groups/Group 18/Homework October 20th, 2010]

-Roland

I've moved the page, it was missing the ''Course:'' part which means it was created directly inside the wiki and not as a subpage of your group page, which is something the wiki admins don't like that much. By the way, you're allowed to use spaces in the name of your pages.

-- [[User:DavidKohler|DavidKohler]] 06:28, 20 October 2010 (UTC)

1-5

Victoria Wall

1.A bus traveled from the terminal to the airport at an average speed of 30 mi/hr and the trip took an hour and 20 min. The bus then traveled from the airport back to the terminal and again averaged 30 mi/hr. However, the return trip required 80 min. Explain.

' 'Lets call the terminal T and the airport A. If the bus travelled from T to A at 30mi/hr and it took them one hour and 20 mins to get from T to A at this speed, and there are 60 minutes in one hour, it took the bus 60min + 20min to get to A which is a total of 80min. The bus took 80 min to get from T to A. To get from A to T at the same speed (30mi/hr) it took the bus 80min. 80min = 80 min. This means going from A to T or vis versa at 30 mi/hr it will take the bus 80min.

2.A lady did not have her driver's license with her when she failed to stop at a stop sign and then went three blocks down a one-way street the wrong way. A policeman saw her, but he did not stop her. Explain.

' 'The lady was walking. It never says she was driving.

3.One of three boxes contains apples, another box contains oranges, and another box contains a mixture of apples and oranges. The boxes are labeled APPLES, ORANGES and APPLES AND ORANGES, but each label is incorrect. Can you select one fruit from only one box and determine the correct labels? Explain.

' 'if you selecet from the box APPLES AND ORANGES then you will be able to see the labels if they are correct or not.

4.I am the brother of the blind fiddler, but brothers I have none. How can this be?

' 'Since it says that he is the brother of the blind fiddler it does not mean that the fiddle is male, since he has no brothers than the fiddler must be a female.

5.Two quarters rest next to each other on a table. One coin is held fixed while the second coin is rolled around the edge of the first coin with no slipping. When the moving coin returns to its original position, how many times has it revolved?

' 'This is because the moving quarters revolves two full revolutions

6-10

Caitlin Lastiwka- Farquharson

6. Three kinds of apples are all mixed up in a basket. How many apples must you draw without (without looking) from the basket to be sure of getting at least two of a kind?

' ' To be sure you are getting at least two of a kind, you must select all of the other types of apples, plus two more. Meaning that only once you have selected all of the other apples can you be sure that you will select two of the kind you desire. It can be written like this: x,a x2, b and x3, c, with x representing the quantity of apples. This can be calculated by x2 + x3 +2. X2 representing one of the types of apples, x3 representing the other type and 2 representing 2 of the kind of apples you are trying to select. This is the only way to be sure you are getting at least two of a kind. ' '

7. Suppose you have 40 blue socks and 40 brown socks in a drawer. How many socks must you take from the drawer (without looking) to be sure of getting (i) a pair of the same colour, and (ii) a pair with different colors.

' 'You must take three socks from the drawer to ensure you have a pair that match. This is because if you only select two, one could be brown and one could be blue. Selecting three, ensures that at least two of them will be the same colour. As for part two, you would need to select 41 socks to ensure you had a pair of different coloured socks because if you select 40 or less you could get all the same colour, but selecting 41 ensures you will have at least one pair of mixed colour. ' '

8. Rueben says "Two days ago I was 20 years old. Later next year I will be 23 years old." Explain how this is possible.

' 'It is possible if your birthday is on the 31st of December and today is the 1st of January. This is because on the 30th of December (two days ago) you we’re 20 years old and now you are 21, later this year you will turn 22 on the 31st of December, and therefore 23 the next year.' '

9. A rope ladder hanging over the side of a boat has rungs one foot apart. Ten rungs are showing. If the tide rises five feet, how many rungs will be showing?

' ' 5 rungs will be showing, because if there are 10 showing now, and they are each a foot apart, then for 5 more rungs to be showing there would need to be an increase in the level of water by 5 feet. ' '

==10.Suppose one-half of all people are chocolate eaters and one-half of all people are women. (i) Does it follow that one-fourth of all people are women chocolate eaters? (ii) Does it follow that one-half of all men are chocolate eaters? Explain. ==

' ' No, it does not follow that one-fourth of all people are women chocolate eaters and it does not follow that half of all men are chocolate eaters because are completely independent scenarios. Meaning that the the amount of women there are does not influence the amount of men that will eat chocolate. For example, If 50% of people are women and 50% of the entire population including men and women eat chocolate (arrived at by using the same logic that if 1/4 of women eat chocolate and 1/4 of men eat chocolate), that entire 50% could be comprised of women, meaning that no men eat chocolate disproving the statement.

==11-14==
==Sifat Hasan==

==11 11. A woman, her older brother, her son, and her daughter are chess players. The worst player’s twin, who is one of the four players, and the best player are of opposite sex. The worst player and the best player have the same age. If this is possible, who is the worst player?==

The four players (according to age, from oldest to youngest) are: woman's older brother, woman, and the son and the daughter (of the same age). Assuming that the children are of the same age (i.e. twins), the worst player is one of them, since they are the only ones who can have a twin. Assuming that the worst player is the daughter, her brother the son, is of the opposite sex as the woman, therefore the woman is the worst player. However, since the worst and the best player are of the same age, this is not possible, because the twins are of the opposite sex and they are of different genders.

==12 A Manhattan fellow had a girlfriend in the Bronx and a girlfriend in Brooklyn. He decided which girlfriend to visit by arriving randomly at the train station and taking the first of the Bronx or Brooklyn trains that arrived. The trains to Brooklyn and the Bronx each arrived regularly every 10 minutes. Not long after he began his scheme the man's Bronx girlfriend left him because he rarely visited. Give a (logical) explanation==

Assuming that the Bronx and the Brooklyn train arrive one after the other every 10 minutes, the only logical explanation would be that the man in Manhattan coincidentally went to the station 10 minutes or less before a train to Brooklyn arrived, most of the time.

==13 If a clock takes 5 seconds to strike 5:00 (with 5 equally spaced chimes), how long does it take to strike 10:00 (with 10 equally spaced chimes)?==

If it takes 5 seconds to strike 5, there will be 4 little halts in the middle. Therefore it takes 5 chimes 4 (5/4) = 1.25 second halts to finish. For 10 chimes, there are 9 halts so, it takes 9x 1.25 = 11.25 seconds for 10 halts.

==14 One day in the maternity ward, the name tags for four girl babies became mixed up. (i) In how many different ways could two of the babies be tagged correctly and two of the babies be tagged incorrectly? (ii) In how many different ways could three of the babies be tagged correctly and one baby be tagged incorrectly?==

(i)and (ii) If we take the babies names as A,B,C and D. There are 6 different combinations of the mix up, that two babies' names can be correct and 2 can be wrong. Assuming the name tags for the babies A,B,C and D are in respective order, they are ABDC, ADCB, ACBD, DBCA, CBAD and BACD. All other combinations for example BCAD will have one correct and 3 incorrect, or all four of them correct, because if 3 are correct, the fourth one has to be correct.

==15-16==
==Roland Will==

==15. Alex says to you, “I'll bet you any amount of money that if I shuffle this deck of cards, there will always be as many red cards in the first half of the deck as there are black cards in the second half of the deck.” Should you accept his bet?==

Answer: No, you shouldn't assuming the deck has equal amounts of red and black cards as in a standard 52 card deck.
Solution: In a standard 52 card deck, half of the cards (26) are black and half are red. If you take 26 cards at random from the deck, x of them will be black and y of them will be red, and x+y=26. As there are 26 of each color in the deck, then x+?=26 for the black cards in the deck and ?+y=26 for the red cards in the deck. As x+y=26 in the first randomly selected 26 cards, then the value of black cards in the other half of the deck must equal y, and the value of red cards in the other half of the deck must equal x meaning that "there will always be as many red cards in the first half of the deck as there are black cards in the second half of the deck."

==16. Suppose that each daughter in your family has the same number of brothers as she has sisters, and each son in your family has twice as many sisters as he has brothers. How many sons and daughters are in the family?==

Answer:3 total, 2 sister and 1 brother
Solution: Since the daughters in the family each have as many brothers as sisters the amount of sisters, with x standing for the amount of brothers, is x+1. As each brother has twice as many sisters as brothers, the amount of sisters must equal 2(x-1) or 2x-2. To find the number of brother: x+1=2x+1, 1=x-2, 3=x, which means that their are 3 brothers and 4 sisters (x+1= the number of sisters and x=3). This makes sense because a sister would have an equal amount of brothers to sisters, 3 sisters and 3 brothers, if there were 4 sisters and 3 brothers total, and each brother would have 4 sisters and 3 brothers, which is twice the amount of brothers to sisters.

==17~21==
==Audrey Chen==

==17.The zero point on a bathroom scale is set incorrectly, but otherwise the scale is accurate. It shows 60 kg when Dan stands on the scale, 50 kg when Sarah stands on the scale, but 105 kg when Dan and Sarah both stand on the scale. Does the scale read too high or too low? Explain. ==

''The scale read too low, since Dan is shown as 60kg and Sarah is 50kg, suppose 60+50=110, 105-110=-5, so that means the scale is smaller than 0 in the beginning''

==18. Alice takes one-third of the pennies from a large jar. Then Bret takes one-third of the remaining pennies from the jar. Finally, Carla takes one-third of the remaining pennies from the jar, leaving 40 pennies in the jar. How many pennies were in the jar at the start? ==

''If the total pennies is "x", Alice take 1/3x, so it has 2/3x left after Alice took it, than Bret take 1/3 out, after Alice took it, which is 2/3x*1/3= 2/9x, so in the beginning they have x, after Alice took it, it has 2/3x left, and Bret took 2/9x, so after Bret took it, it becomes 2/3x-2/9x= 4/9x-2/9x=2/9x left in the jar. Than Carla take 1/3 of the rest, so she took 1/3 of rest which is 2/9x*1/3=3/27x, so Alice took 1/3x, Bret tool 2/9x, Carla took 3/27x, three of them totaly took 1/3x+2/9x+3/27x=18/27x, so there still has x-18/27x= 9/27x= 1/3 left, 1/3x=40pennies, so x=120 pennies, so it was having 120 pennies in the jar.

==19. One morning each member of Angela's family drank an eight-ounce cup of coffee and milk, with the (nonzero) amounts of coffee and milk varying from cup to cup. Angela drank a quarter of the total amount of milk and a sixth of the total amount of coffee. What is the least number of people in the family? ==

''If we let total milk is x, total coffee is y. Than 1/4x+1/6y=8, and because every cup is 8ounce, x+y is multiple by 8. So make it easier, we use 1/4x+1/6y=8 * 12 to both sides. than we will got 3x+2y=96, now we have 3x+2y=96 and x+y is multiple of 8, and the number that multiple by 8 is 8, 16, 24, 32... so 2x+2y= 16, 32, 48, 64, 80, 96, since 3x+2y=96, it can't be more than 96. It will only have 6 possible number, so if you take 3x+2y=96 substracting 2x+2y=16, 32, 48, 64, 80, 96 you can get 6 possible x, which are 80, 64, 48, 32, 16, and 0. Than put the number into 3x+2y=96, if you put 80 in, will get 20, which is bigger than 8, and also 64, 48. If we use 32, it will equal to 8, but that means we have 0 coffee, but coffee can't be 0, so there's only 16 and 0 left. Since Angela had 1/4 of total amount of milk, milk can't be 0. So we got 16ounce than 16*(1/4)=4, so that means she had 8-4=4 's coffee. So 4=1/6 coffee, than the total amount of coffee would be 4*6=24. than x=16 and y=24, 16+24=40 40/8ounce=5, so at least have 5 cups of drinks, so that means at least they have 5 members in Angela's family.''

==20.Of two clocks next to each other, one runs 5 min per hour fast and the other runs 5 min per hour slow. At midnight the clocks show the same time. At what time are they are one hour apart? ==

''Since one clock runs 5 min faster per hour, the other is 5 min slower, after clock runs an hour, two clocks will have 10 min different from each other. 60 min an hour. 60/10=6, so after 6 hours two clocks will having one hour apart, and that would be 6AM.''

==21.Sven placed exactly in the middle among all runners in a race. Dan was slower than Sven, in 10th place, and Lars was in 16th place. How many runners were in the race? ==

''There were 17 runners. Since lars was in 16th place, the runners at least have to be 16, than if Sven is placed exactly in the middle, it means it would have even number of runners. Because Dan is slower and he was at 10 place that tells us Seven has to be before 10th, and if there has 19 runners, Sven and Dan would be at the same place, so it should be 17 runners, than Sven would be at exactly in the middle which at 9th place.''

==22-25==

Roland Will

22. During a vacation, it rained on 13 days, but when it rained in the morning, the afternoon was sunny, and every rainy afternoon was preceded by a sunny morning. There were 11 sunny mornings and 12 sunny afternoons. How long was the vacation?

Answer: 18 days of vacation.

Solution: 13 of the days of vacation were half sunny and half rainy. As there were 23 sunny mornings and afternoons (11 sunny mornings+12 sunny afternoons = 23 sunny mornings and afternoons), 13 of those sunny afternoons or mornings were on half rainy days. This means there are 10 sunny half-days left over, which equal 5 sunny full days. The 5 sunny full days plus the 13 half sunny/rainy days equal 18 total days of vacation.

23. Suppose you overhear the following conversation: Paul: How old are your three children? Paula: The product of their ages is 36 and the sum of their ages is the same as today's date. Paul: That is not enough information. Paula: The oldest child also has red hair. If you were Paul could you determine the ages of Paula's children? Explain.

Answer: If I were Paul this might be possible, but since we don’t know the date that Paula said this, it is not possible for us to find out.

Solution: There are many different combinations of three numbers that can be multiplied and will produce 36. As we do not know the date that Paula said this, the only thing we can be sure of is that the sum of the ages is less than 31 because no month has more than 31 days. Unfortunately, only one set of ages (ages 1 year old, 1 year old and 36 years old) has a sum greater than 31, which leaves many possible combinations open as possible. For today’s date, the 13th, ages of 2, 2, and 9 would produce 36 and have a sum of 13, but, again, it is uncertain. If it were the first of the month, there would be no possible combinations that would produce 36 and sum 1.

24. Two candles of equal length were lit at the same time. One candle took 6 hr to burn out and the other candle took 3 hr to burn out. After how much time was one candle exactly twice as long as the other candle?

Answer: 2 hours.

Solution: The faster burning candle took half the time to burn as the slower burning candle (3 hours/ 6 hours = 1/2), meaning it burned twice as fast. This means that after 2/3 of the total burning time for the faster burning candle it will be 1/3 of its original height and at the slower burning candle will be at 2/3 of its original height and 1/3 is half of 2/3. Since the faster burning candle took 3 hours to burn, 2/3 of its total burning time is 2 hours.

25. Two candles of length L and L + 1 were lit at 6:00 and 4:30, respectively. At 8:30 they had the same length. The longer candle died at 10:30 and the shorter candle died at 10:00. Find L.

Answer: L=2.

Solution: The shorter candle lasted for 4 hours and the longer candle lasted for 6 hours. As 6 hours – 4 hours = 2 hours and 2 hours / 4 hours = 1/2, the longer candle lasted 50% longer and was, therefore, 50% longer in length. This means that the +1 in L+1 on the longer candle was 1/2 of L. 1/2L=1, so L=2*1, L=2.

Course:MATH110/Archive/2010-2011/003/Groups/Group 18

2010-11-12T05:24:09Z

RolandWill: /* 8. Rueben says "Two days ago I was 20 years old. Later next year I will be 23 years old." Explain how this is possible. */

{{Infobox MATH110 Groups
| group number = 18
| member 1 = [[User:ChouJuChen|Audrey Chen]]
| member 2 = [[User:SifatHasan|Sifat Hasan]]
| member 3 = [[User:CaitlinLastiwkaFarquharson|Caitlin Lastiwka-Farquharson]]
| member 4 = [[User:VictoriaWall|Victoria Wall]]
| member 5 = [[User:RolandWill|Roland Will]]
| member 6 =
}}

==Sub-Pages==

Basic Skills Project [http://wiki.ubc.ca/Course:MATH110/003/Groups/Group_18/Basic_Skills_Project]

==Homework due October 20th, 2010==

I created a page for our homework due tomorrow: [http://wiki.ubc.ca/Course:MATH110/003/Groups/Group_18/Homework_October_20th,_2010 http://wiki.ubc.ca/Course:MATH110/003/Groups/Group 18/Homework October 20th, 2010]

-Roland

I've moved the page, it was missing the ''Course:'' part which means it was created directly inside the wiki and not as a subpage of your group page, which is something the wiki admins don't like that much. By the way, you're allowed to use spaces in the name of your pages.

-- [[User:DavidKohler|DavidKohler]] 06:28, 20 October 2010 (UTC)

1-5

Victoria Wall

1.A bus traveled from the terminal to the airport at an average speed of 30 mi/hr and the trip took an hour and 20 min. The bus then traveled from the airport back to the terminal and again averaged 30 mi/hr. However, the return trip required 80 min. Explain.

' 'Lets call the terminal T and the airport A. If the bus travelled from T to A at 30mi/hr and it took them one hour and 20 mins to get from T to A at this speed, and there are 60 minutes in one hour, it took the bus 60min + 20min to get to A which is a total of 80min. The bus took 80 min to get from T to A. To get from A to T at the same speed (30mi/hr) it took the bus 80min. 80min = 80 min. This means going from A to T or vis versa at 30 mi/hr it will take the bus 80min.

2.A lady did not have her driver's license with her when she failed to stop at a stop sign and then went three blocks down a one-way street the wrong way. A policeman saw her, but he did not stop her. Explain.

' 'The lady was walking. It never says she was driving.

3.One of three boxes contains apples, another box contains oranges, and another box contains a mixture of apples and oranges. The boxes are labeled APPLES, ORANGES and APPLES AND ORANGES, but each label is incorrect. Can you select one fruit from only one box and determine the correct labels? Explain.

' 'if you selecet from the box APPLES AND ORANGES then you will be able to see the labels if they are correct or not.

4.I am the brother of the blind fiddler, but brothers I have none. How can this be?

' 'Since it says that he is the brother of the blind fiddler it does not mean that the fiddle is male, since he has no brothers than the fiddler must be a female.

5.Two quarters rest next to each other on a table. One coin is held fixed while the second coin is rolled around the edge of the first coin with no slipping. When the moving coin returns to its original position, how many times has it revolved?

' 'This is because the moving quarters revolves two full revolutions

6-10

Caitlin Lastiwka- Farquharson

6. Three kinds of apples are all mixed up in a basket. How many apples must you draw without (without looking) from the basket to be sure of getting at least two of a kind?

' ' To be sure you are getting at least two of a kind, you must select all of the other types of apples, plus two more. Meaning that only once you have selected all of the other apples can you be sure that you will select two of the kind you desire. It can be written like this: x,a x2, b and x3, c, with x representing the quantity of apples. This can be calculated by x2 + x3 +2. X2 representing one of the types of apples, x3 representing the other type and 2 representing 2 of the kind of apples you are trying to select. This is the only way to be sure you are getting at least two of a kind. ' '

7. Suppose you have 40 blue socks and 40 brown socks in a drawer. How many socks must you take from the drawer (without looking) to be sure of getting (i) a pair of the same colour, and (ii) a pair with different colors.

' 'You must take three socks from the drawer to ensure you have a pair that match. This is because if you only select two, one could be brown and one could be blue. Selecting three, ensures that at least two of them will be the same colour. As for part two, you would need to select 41 socks to ensure you had a pair of different coloured socks because if you select 40 or less you could get all the same colour, but selecting 41 ensures you will have at least one pair of mixed colour. ' '

8. Rueben says "Two days ago I was 20 years old. Later next year I will be 23 years old." Explain how this is possible.

' 'It is possible if your birthday is on the 31st of December and today is the 1st of January. This is because on the 30th of December (two days ago) you we’re 20 years old and now you are 21, later this year you will turn 22 on the 31st of December, and therefore 23 the next year.' '

==9. A rope ladder hanging over the side of a boat has rungs one foot apart. Ten rungs are showing. If the tide rises five feet, how many rungs will be showing? ==

' ' 5 rungs will be showing, because if there are 10 showing now, and they are each a foot apart, then for 5 more rungs to be showing there would need to be an increase in the level of water by 5 feet. ' '

==10.Suppose one-half of all people are chocolate eaters and one-half of all people are women. (i) Does it follow that one-fourth of all people are women chocolate eaters? (ii) Does it follow that one-half of all men are chocolate eaters? Explain. ==

' ' No, it does not follow that one-fourth of all people are women chocolate eaters and it does not follow that half of all men are chocolate eaters because are completely independent scenarios. Meaning that the the amount of women there are does not influence the amount of men that will eat chocolate. For example, If 50% of people are women and 50% of the entire population including men and women eat chocolate (arrived at by using the same logic that if 1/4 of women eat chocolate and 1/4 of men eat chocolate), that entire 50% could be comprised of women, meaning that no men eat chocolate disproving the statement.

==11-14==
==Sifat Hasan==

==11 11. A woman, her older brother, her son, and her daughter are chess players. The worst player’s twin, who is one of the four players, and the best player are of opposite sex. The worst player and the best player have the same age. If this is possible, who is the worst player?==

The four players (according to age, from oldest to youngest) are: woman's older brother, woman, and the son and the daughter (of the same age). Assuming that the children are of the same age (i.e. twins), the worst player is one of them, since they are the only ones who can have a twin. Assuming that the worst player is the daughter, her brother the son, is of the opposite sex as the woman, therefore the woman is the worst player. However, since the worst and the best player are of the same age, this is not possible, because the twins are of the opposite sex and they are of different genders.

==12 A Manhattan fellow had a girlfriend in the Bronx and a girlfriend in Brooklyn. He decided which girlfriend to visit by arriving randomly at the train station and taking the first of the Bronx or Brooklyn trains that arrived. The trains to Brooklyn and the Bronx each arrived regularly every 10 minutes. Not long after he began his scheme the man's Bronx girlfriend left him because he rarely visited. Give a (logical) explanation==

Assuming that the Bronx and the Brooklyn train arrive one after the other every 10 minutes, the only logical explanation would be that the man in Manhattan coincidentally went to the station 10 minutes or less before a train to Brooklyn arrived, most of the time.

==13 If a clock takes 5 seconds to strike 5:00 (with 5 equally spaced chimes), how long does it take to strike 10:00 (with 10 equally spaced chimes)?==

If it takes 5 seconds to strike 5, there will be 4 little halts in the middle. Therefore it takes 5 chimes 4 (5/4) = 1.25 second halts to finish. For 10 chimes, there are 9 halts so, it takes 9x 1.25 = 11.25 seconds for 10 halts.

==14 One day in the maternity ward, the name tags for four girl babies became mixed up. (i) In how many different ways could two of the babies be tagged correctly and two of the babies be tagged incorrectly? (ii) In how many different ways could three of the babies be tagged correctly and one baby be tagged incorrectly?==

(i)and (ii) If we take the babies names as A,B,C and D. There are 6 different combinations of the mix up, that two babies' names can be correct and 2 can be wrong. Assuming the name tags for the babies A,B,C and D are in respective order, they are ABDC, ADCB, ACBD, DBCA, CBAD and BACD. All other combinations for example BCAD will have one correct and 3 incorrect, or all four of them correct, because if 3 are correct, the fourth one has to be correct.

==15-16==
==Roland Will==

==15. Alex says to you, “I'll bet you any amount of money that if I shuffle this deck of cards, there will always be as many red cards in the first half of the deck as there are black cards in the second half of the deck.” Should you accept his bet?==

Answer: No, you shouldn't assuming the deck has equal amounts of red and black cards as in a standard 52 card deck.
Solution: In a standard 52 card deck, half of the cards (26) are black and half are red. If you take 26 cards at random from the deck, x of them will be black and y of them will be red, and x+y=26. As there are 26 of each color in the deck, then x+?=26 for the black cards in the deck and ?+y=26 for the red cards in the deck. As x+y=26 in the first randomly selected 26 cards, then the value of black cards in the other half of the deck must equal y, and the value of red cards in the other half of the deck must equal x meaning that "there will always be as many red cards in the first half of the deck as there are black cards in the second half of the deck."

==16. Suppose that each daughter in your family has the same number of brothers as she has sisters, and each son in your family has twice as many sisters as he has brothers. How many sons and daughters are in the family?==

Answer:3 total, 2 sister and 1 brother
Solution: Since the daughters in the family each have as many brothers as sisters the amount of sisters, with x standing for the amount of brothers, is x+1. As each brother has twice as many sisters as brothers, the amount of sisters must equal 2(x-1) or 2x-2. To find the number of brother: x+1=2x+1, 1=x-2, 3=x, which means that their are 3 brothers and 4 sisters (x+1= the number of sisters and x=3). This makes sense because a sister would have an equal amount of brothers to sisters, 3 sisters and 3 brothers, if there were 4 sisters and 3 brothers total, and each brother would have 4 sisters and 3 brothers, which is twice the amount of brothers to sisters.

==17~21==
==Audrey Chen==

==17.The zero point on a bathroom scale is set incorrectly, but otherwise the scale is accurate. It shows 60 kg when Dan stands on the scale, 50 kg when Sarah stands on the scale, but 105 kg when Dan and Sarah both stand on the scale. Does the scale read too high or too low? Explain. ==

''The scale read too low, since Dan is shown as 60kg and Sarah is 50kg, suppose 60+50=110, 105-110=-5, so that means the scale is smaller than 0 in the beginning''

==18. Alice takes one-third of the pennies from a large jar. Then Bret takes one-third of the remaining pennies from the jar. Finally, Carla takes one-third of the remaining pennies from the jar, leaving 40 pennies in the jar. How many pennies were in the jar at the start? ==

''If the total pennies is "x", Alice take 1/3x, so it has 2/3x left after Alice took it, than Bret take 1/3 out, after Alice took it, which is 2/3x*1/3= 2/9x, so in the beginning they have x, after Alice took it, it has 2/3x left, and Bret took 2/9x, so after Bret took it, it becomes 2/3x-2/9x= 4/9x-2/9x=2/9x left in the jar. Than Carla take 1/3 of the rest, so she took 1/3 of rest which is 2/9x*1/3=3/27x, so Alice took 1/3x, Bret tool 2/9x, Carla took 3/27x, three of them totaly took 1/3x+2/9x+3/27x=18/27x, so there still has x-18/27x= 9/27x= 1/3 left, 1/3x=40pennies, so x=120 pennies, so it was having 120 pennies in the jar.

==19. One morning each member of Angela's family drank an eight-ounce cup of coffee and milk, with the (nonzero) amounts of coffee and milk varying from cup to cup. Angela drank a quarter of the total amount of milk and a sixth of the total amount of coffee. What is the least number of people in the family? ==

''If we let total milk is x, total coffee is y. Than 1/4x+1/6y=8, and because every cup is 8ounce, x+y is multiple by 8. So make it easier, we use 1/4x+1/6y=8 * 12 to both sides. than we will got 3x+2y=96, now we have 3x+2y=96 and x+y is multiple of 8, and the number that multiple by 8 is 8, 16, 24, 32... so 2x+2y= 16, 32, 48, 64, 80, 96, since 3x+2y=96, it can't be more than 96. It will only have 6 possible number, so if you take 3x+2y=96 substracting 2x+2y=16, 32, 48, 64, 80, 96 you can get 6 possible x, which are 80, 64, 48, 32, 16, and 0. Than put the number into 3x+2y=96, if you put 80 in, will get 20, which is bigger than 8, and also 64, 48. If we use 32, it will equal to 8, but that means we have 0 coffee, but coffee can't be 0, so there's only 16 and 0 left. Since Angela had 1/4 of total amount of milk, milk can't be 0. So we got 16ounce than 16*(1/4)=4, so that means she had 8-4=4 's coffee. So 4=1/6 coffee, than the total amount of coffee would be 4*6=24. than x=16 and y=24, 16+24=40 40/8ounce=5, so at least have 5 cups of drinks, so that means at least they have 5 members in Angela's family.''

==20.Of two clocks next to each other, one runs 5 min per hour fast and the other runs 5 min per hour slow. At midnight the clocks show the same time. At what time are they are one hour apart? ==

''Since one clock runs 5 min faster per hour, the other is 5 min slower, after clock runs an hour, two clocks will have 10 min different from each other. 60 min an hour. 60/10=6, so after 6 hours two clocks will having one hour apart, and that would be 6AM.''

==21.Sven placed exactly in the middle among all runners in a race. Dan was slower than Sven, in 10th place, and Lars was in 16th place. How many runners were in the race? ==

''There were 17 runners. Since lars was in 16th place, the runners at least have to be 16, than if Sven is placed exactly in the middle, it means it would have even number of runners. Because Dan is slower and he was at 10 place that tells us Seven has to be before 10th, and if there has 19 runners, Sven and Dan would be at the same place, so it should be 17 runners, than Sven would be at exactly in the middle which at 9th place.''

==22-25==

Roland Will

22. During a vacation, it rained on 13 days, but when it rained in the morning, the afternoon was sunny, and every rainy afternoon was preceded by a sunny morning. There were 11 sunny mornings and 12 sunny afternoons. How long was the vacation?

Answer: 18 days of vacation.

Solution: 13 of the days of vacation were half sunny and half rainy. As there were 23 sunny mornings and afternoons (11 sunny mornings+12 sunny afternoons = 23 sunny mornings and afternoons), 13 of those sunny afternoons or mornings were on half rainy days. This means there are 10 sunny half-days left over, which equal 5 sunny full days. The 5 sunny full days plus the 13 half sunny/rainy days equal 18 total days of vacation.

23. Suppose you overhear the following conversation: Paul: How old are your three children? Paula: The product of their ages is 36 and the sum of their ages is the same as today's date. Paul: That is not enough information. Paula: The oldest child also has red hair. If you were Paul could you determine the ages of Paula's children? Explain.

Answer: If I were Paul this might be possible, but since we don’t know the date that Paula said this, it is not possible for us to find out.

Solution: There are many different combinations of three numbers that can be multiplied and will produce 36. As we do not know the date that Paula said this, the only thing we can be sure of is that the sum of the ages is less than 31 because no month has more than 31 days. Unfortunately, only one set of ages (ages 1 year old, 1 year old and 36 years old) has a sum greater than 31, which leaves many possible combinations open as possible. For today’s date, the 13th, ages of 2, 2, and 9 would produce 36 and have a sum of 13, but, again, it is uncertain. If it were the first of the month, there would be no possible combinations that would produce 36 and sum 1.

24. Two candles of equal length were lit at the same time. One candle took 6 hr to burn out and the other candle took 3 hr to burn out. After how much time was one candle exactly twice as long as the other candle?

Answer: 2 hours.

Solution: The faster burning candle took half the time to burn as the slower burning candle (3 hours/ 6 hours = 1/2), meaning it burned twice as fast. This means that after 2/3 of the total burning time for the faster burning candle it will be 1/3 of its original height and at the slower burning candle will be at 2/3 of its original height and 1/3 is half of 2/3. Since the faster burning candle took 3 hours to burn, 2/3 of its total burning time is 2 hours.

25. Two candles of length L and L + 1 were lit at 6:00 and 4:30, respectively. At 8:30 they had the same length. The longer candle died at 10:30 and the shorter candle died at 10:00. Find L.

Answer: L=2.

Solution: The shorter candle lasted for 4 hours and the longer candle lasted for 6 hours. As 6 hours – 4 hours = 2 hours and 2 hours / 4 hours = 1/2, the longer candle lasted 50% longer and was, therefore, 50% longer in length. This means that the +1 in L+1 on the longer candle was 1/2 of L. 1/2L=1, so L=2*1, L=2.

Course:MATH110/Archive/2010-2011/003/Groups/Group 18

2010-11-12T05:23:59Z

RolandWill: /* 7. Suppose you have 40 blue socks and 40 brown socks in a drawer. How many socks must you take from the drawer (without looking) to be sure of getting (i) a pair of the same colour, and (ii) a pair with different colors. */

{{Infobox MATH110 Groups
| group number = 18
| member 1 = [[User:ChouJuChen|Audrey Chen]]
| member 2 = [[User:SifatHasan|Sifat Hasan]]
| member 3 = [[User:CaitlinLastiwkaFarquharson|Caitlin Lastiwka-Farquharson]]
| member 4 = [[User:VictoriaWall|Victoria Wall]]
| member 5 = [[User:RolandWill|Roland Will]]
| member 6 =
}}

==Sub-Pages==

Basic Skills Project [http://wiki.ubc.ca/Course:MATH110/003/Groups/Group_18/Basic_Skills_Project]

==Homework due October 20th, 2010==

I created a page for our homework due tomorrow: [http://wiki.ubc.ca/Course:MATH110/003/Groups/Group_18/Homework_October_20th,_2010 http://wiki.ubc.ca/Course:MATH110/003/Groups/Group 18/Homework October 20th, 2010]

-Roland

I've moved the page, it was missing the ''Course:'' part which means it was created directly inside the wiki and not as a subpage of your group page, which is something the wiki admins don't like that much. By the way, you're allowed to use spaces in the name of your pages.

-- [[User:DavidKohler|DavidKohler]] 06:28, 20 October 2010 (UTC)

1-5

Victoria Wall

1.A bus traveled from the terminal to the airport at an average speed of 30 mi/hr and the trip took an hour and 20 min. The bus then traveled from the airport back to the terminal and again averaged 30 mi/hr. However, the return trip required 80 min. Explain.

' 'Lets call the terminal T and the airport A. If the bus travelled from T to A at 30mi/hr and it took them one hour and 20 mins to get from T to A at this speed, and there are 60 minutes in one hour, it took the bus 60min + 20min to get to A which is a total of 80min. The bus took 80 min to get from T to A. To get from A to T at the same speed (30mi/hr) it took the bus 80min. 80min = 80 min. This means going from A to T or vis versa at 30 mi/hr it will take the bus 80min.

2.A lady did not have her driver's license with her when she failed to stop at a stop sign and then went three blocks down a one-way street the wrong way. A policeman saw her, but he did not stop her. Explain.

' 'The lady was walking. It never says she was driving.

3.One of three boxes contains apples, another box contains oranges, and another box contains a mixture of apples and oranges. The boxes are labeled APPLES, ORANGES and APPLES AND ORANGES, but each label is incorrect. Can you select one fruit from only one box and determine the correct labels? Explain.

' 'if you selecet from the box APPLES AND ORANGES then you will be able to see the labels if they are correct or not.

4.I am the brother of the blind fiddler, but brothers I have none. How can this be?

' 'Since it says that he is the brother of the blind fiddler it does not mean that the fiddle is male, since he has no brothers than the fiddler must be a female.

5.Two quarters rest next to each other on a table. One coin is held fixed while the second coin is rolled around the edge of the first coin with no slipping. When the moving coin returns to its original position, how many times has it revolved?

' 'This is because the moving quarters revolves two full revolutions

6-10

Caitlin Lastiwka- Farquharson

6. Three kinds of apples are all mixed up in a basket. How many apples must you draw without (without looking) from the basket to be sure of getting at least two of a kind?

' ' To be sure you are getting at least two of a kind, you must select all of the other types of apples, plus two more. Meaning that only once you have selected all of the other apples can you be sure that you will select two of the kind you desire. It can be written like this: x,a x2, b and x3, c, with x representing the quantity of apples. This can be calculated by x2 + x3 +2. X2 representing one of the types of apples, x3 representing the other type and 2 representing 2 of the kind of apples you are trying to select. This is the only way to be sure you are getting at least two of a kind. ' '

7. Suppose you have 40 blue socks and 40 brown socks in a drawer. How many socks must you take from the drawer (without looking) to be sure of getting (i) a pair of the same colour, and (ii) a pair with different colors.

' 'You must take three socks from the drawer to ensure you have a pair that match. This is because if you only select two, one could be brown and one could be blue. Selecting three, ensures that at least two of them will be the same colour. As for part two, you would need to select 41 socks to ensure you had a pair of different coloured socks because if you select 40 or less you could get all the same colour, but selecting 41 ensures you will have at least one pair of mixed colour. ' '

==8. Rueben says "Two days ago I was 20 years old. Later next year I will be 23 years old." Explain how this is possible. ==

' 'It is possible if your birthday is on the 31st of December and today is the 1st of January. This is because on the 30th of December (two days ago) you we’re 20 years old and now you are 21, later this year you will turn 22 on the 31st of December, and therefore 23 the next year.' '

==9. A rope ladder hanging over the side of a boat has rungs one foot apart. Ten rungs are showing. If the tide rises five feet, how many rungs will be showing? ==

' ' 5 rungs will be showing, because if there are 10 showing now, and they are each a foot apart, then for 5 more rungs to be showing there would need to be an increase in the level of water by 5 feet. ' '

==10.Suppose one-half of all people are chocolate eaters and one-half of all people are women. (i) Does it follow that one-fourth of all people are women chocolate eaters? (ii) Does it follow that one-half of all men are chocolate eaters? Explain. ==

' ' No, it does not follow that one-fourth of all people are women chocolate eaters and it does not follow that half of all men are chocolate eaters because are completely independent scenarios. Meaning that the the amount of women there are does not influence the amount of men that will eat chocolate. For example, If 50% of people are women and 50% of the entire population including men and women eat chocolate (arrived at by using the same logic that if 1/4 of women eat chocolate and 1/4 of men eat chocolate), that entire 50% could be comprised of women, meaning that no men eat chocolate disproving the statement.

==11-14==
==Sifat Hasan==

==11 11. A woman, her older brother, her son, and her daughter are chess players. The worst player’s twin, who is one of the four players, and the best player are of opposite sex. The worst player and the best player have the same age. If this is possible, who is the worst player?==

The four players (according to age, from oldest to youngest) are: woman's older brother, woman, and the son and the daughter (of the same age). Assuming that the children are of the same age (i.e. twins), the worst player is one of them, since they are the only ones who can have a twin. Assuming that the worst player is the daughter, her brother the son, is of the opposite sex as the woman, therefore the woman is the worst player. However, since the worst and the best player are of the same age, this is not possible, because the twins are of the opposite sex and they are of different genders.

==12 A Manhattan fellow had a girlfriend in the Bronx and a girlfriend in Brooklyn. He decided which girlfriend to visit by arriving randomly at the train station and taking the first of the Bronx or Brooklyn trains that arrived. The trains to Brooklyn and the Bronx each arrived regularly every 10 minutes. Not long after he began his scheme the man's Bronx girlfriend left him because he rarely visited. Give a (logical) explanation==

Assuming that the Bronx and the Brooklyn train arrive one after the other every 10 minutes, the only logical explanation would be that the man in Manhattan coincidentally went to the station 10 minutes or less before a train to Brooklyn arrived, most of the time.

==13 If a clock takes 5 seconds to strike 5:00 (with 5 equally spaced chimes), how long does it take to strike 10:00 (with 10 equally spaced chimes)?==

If it takes 5 seconds to strike 5, there will be 4 little halts in the middle. Therefore it takes 5 chimes 4 (5/4) = 1.25 second halts to finish. For 10 chimes, there are 9 halts so, it takes 9x 1.25 = 11.25 seconds for 10 halts.

==14 One day in the maternity ward, the name tags for four girl babies became mixed up. (i) In how many different ways could two of the babies be tagged correctly and two of the babies be tagged incorrectly? (ii) In how many different ways could three of the babies be tagged correctly and one baby be tagged incorrectly?==

(i)and (ii) If we take the babies names as A,B,C and D. There are 6 different combinations of the mix up, that two babies' names can be correct and 2 can be wrong. Assuming the name tags for the babies A,B,C and D are in respective order, they are ABDC, ADCB, ACBD, DBCA, CBAD and BACD. All other combinations for example BCAD will have one correct and 3 incorrect, or all four of them correct, because if 3 are correct, the fourth one has to be correct.

==15-16==
==Roland Will==

==15. Alex says to you, “I'll bet you any amount of money that if I shuffle this deck of cards, there will always be as many red cards in the first half of the deck as there are black cards in the second half of the deck.” Should you accept his bet?==

Answer: No, you shouldn't assuming the deck has equal amounts of red and black cards as in a standard 52 card deck.
Solution: In a standard 52 card deck, half of the cards (26) are black and half are red. If you take 26 cards at random from the deck, x of them will be black and y of them will be red, and x+y=26. As there are 26 of each color in the deck, then x+?=26 for the black cards in the deck and ?+y=26 for the red cards in the deck. As x+y=26 in the first randomly selected 26 cards, then the value of black cards in the other half of the deck must equal y, and the value of red cards in the other half of the deck must equal x meaning that "there will always be as many red cards in the first half of the deck as there are black cards in the second half of the deck."

==16. Suppose that each daughter in your family has the same number of brothers as she has sisters, and each son in your family has twice as many sisters as he has brothers. How many sons and daughters are in the family?==

Answer:3 total, 2 sister and 1 brother
Solution: Since the daughters in the family each have as many brothers as sisters the amount of sisters, with x standing for the amount of brothers, is x+1. As each brother has twice as many sisters as brothers, the amount of sisters must equal 2(x-1) or 2x-2. To find the number of brother: x+1=2x+1, 1=x-2, 3=x, which means that their are 3 brothers and 4 sisters (x+1= the number of sisters and x=3). This makes sense because a sister would have an equal amount of brothers to sisters, 3 sisters and 3 brothers, if there were 4 sisters and 3 brothers total, and each brother would have 4 sisters and 3 brothers, which is twice the amount of brothers to sisters.

==17~21==
==Audrey Chen==

==17.The zero point on a bathroom scale is set incorrectly, but otherwise the scale is accurate. It shows 60 kg when Dan stands on the scale, 50 kg when Sarah stands on the scale, but 105 kg when Dan and Sarah both stand on the scale. Does the scale read too high or too low? Explain. ==

''The scale read too low, since Dan is shown as 60kg and Sarah is 50kg, suppose 60+50=110, 105-110=-5, so that means the scale is smaller than 0 in the beginning''

==18. Alice takes one-third of the pennies from a large jar. Then Bret takes one-third of the remaining pennies from the jar. Finally, Carla takes one-third of the remaining pennies from the jar, leaving 40 pennies in the jar. How many pennies were in the jar at the start? ==

''If the total pennies is "x", Alice take 1/3x, so it has 2/3x left after Alice took it, than Bret take 1/3 out, after Alice took it, which is 2/3x*1/3= 2/9x, so in the beginning they have x, after Alice took it, it has 2/3x left, and Bret took 2/9x, so after Bret took it, it becomes 2/3x-2/9x= 4/9x-2/9x=2/9x left in the jar. Than Carla take 1/3 of the rest, so she took 1/3 of rest which is 2/9x*1/3=3/27x, so Alice took 1/3x, Bret tool 2/9x, Carla took 3/27x, three of them totaly took 1/3x+2/9x+3/27x=18/27x, so there still has x-18/27x= 9/27x= 1/3 left, 1/3x=40pennies, so x=120 pennies, so it was having 120 pennies in the jar.

==19. One morning each member of Angela's family drank an eight-ounce cup of coffee and milk, with the (nonzero) amounts of coffee and milk varying from cup to cup. Angela drank a quarter of the total amount of milk and a sixth of the total amount of coffee. What is the least number of people in the family? ==

''If we let total milk is x, total coffee is y. Than 1/4x+1/6y=8, and because every cup is 8ounce, x+y is multiple by 8. So make it easier, we use 1/4x+1/6y=8 * 12 to both sides. than we will got 3x+2y=96, now we have 3x+2y=96 and x+y is multiple of 8, and the number that multiple by 8 is 8, 16, 24, 32... so 2x+2y= 16, 32, 48, 64, 80, 96, since 3x+2y=96, it can't be more than 96. It will only have 6 possible number, so if you take 3x+2y=96 substracting 2x+2y=16, 32, 48, 64, 80, 96 you can get 6 possible x, which are 80, 64, 48, 32, 16, and 0. Than put the number into 3x+2y=96, if you put 80 in, will get 20, which is bigger than 8, and also 64, 48. If we use 32, it will equal to 8, but that means we have 0 coffee, but coffee can't be 0, so there's only 16 and 0 left. Since Angela had 1/4 of total amount of milk, milk can't be 0. So we got 16ounce than 16*(1/4)=4, so that means she had 8-4=4 's coffee. So 4=1/6 coffee, than the total amount of coffee would be 4*6=24. than x=16 and y=24, 16+24=40 40/8ounce=5, so at least have 5 cups of drinks, so that means at least they have 5 members in Angela's family.''

==20.Of two clocks next to each other, one runs 5 min per hour fast and the other runs 5 min per hour slow. At midnight the clocks show the same time. At what time are they are one hour apart? ==

''Since one clock runs 5 min faster per hour, the other is 5 min slower, after clock runs an hour, two clocks will have 10 min different from each other. 60 min an hour. 60/10=6, so after 6 hours two clocks will having one hour apart, and that would be 6AM.''

==21.Sven placed exactly in the middle among all runners in a race. Dan was slower than Sven, in 10th place, and Lars was in 16th place. How many runners were in the race? ==

''There were 17 runners. Since lars was in 16th place, the runners at least have to be 16, than if Sven is placed exactly in the middle, it means it would have even number of runners. Because Dan is slower and he was at 10 place that tells us Seven has to be before 10th, and if there has 19 runners, Sven and Dan would be at the same place, so it should be 17 runners, than Sven would be at exactly in the middle which at 9th place.''

==22-25==

Roland Will

22. During a vacation, it rained on 13 days, but when it rained in the morning, the afternoon was sunny, and every rainy afternoon was preceded by a sunny morning. There were 11 sunny mornings and 12 sunny afternoons. How long was the vacation?

Answer: 18 days of vacation.

Solution: 13 of the days of vacation were half sunny and half rainy. As there were 23 sunny mornings and afternoons (11 sunny mornings+12 sunny afternoons = 23 sunny mornings and afternoons), 13 of those sunny afternoons or mornings were on half rainy days. This means there are 10 sunny half-days left over, which equal 5 sunny full days. The 5 sunny full days plus the 13 half sunny/rainy days equal 18 total days of vacation.

23. Suppose you overhear the following conversation: Paul: How old are your three children? Paula: The product of their ages is 36 and the sum of their ages is the same as today's date. Paul: That is not enough information. Paula: The oldest child also has red hair. If you were Paul could you determine the ages of Paula's children? Explain.

Answer: If I were Paul this might be possible, but since we don’t know the date that Paula said this, it is not possible for us to find out.

Solution: There are many different combinations of three numbers that can be multiplied and will produce 36. As we do not know the date that Paula said this, the only thing we can be sure of is that the sum of the ages is less than 31 because no month has more than 31 days. Unfortunately, only one set of ages (ages 1 year old, 1 year old and 36 years old) has a sum greater than 31, which leaves many possible combinations open as possible. For today’s date, the 13th, ages of 2, 2, and 9 would produce 36 and have a sum of 13, but, again, it is uncertain. If it were the first of the month, there would be no possible combinations that would produce 36 and sum 1.

24. Two candles of equal length were lit at the same time. One candle took 6 hr to burn out and the other candle took 3 hr to burn out. After how much time was one candle exactly twice as long as the other candle?

Answer: 2 hours.

Solution: The faster burning candle took half the time to burn as the slower burning candle (3 hours/ 6 hours = 1/2), meaning it burned twice as fast. This means that after 2/3 of the total burning time for the faster burning candle it will be 1/3 of its original height and at the slower burning candle will be at 2/3 of its original height and 1/3 is half of 2/3. Since the faster burning candle took 3 hours to burn, 2/3 of its total burning time is 2 hours.

25. Two candles of length L and L + 1 were lit at 6:00 and 4:30, respectively. At 8:30 they had the same length. The longer candle died at 10:30 and the shorter candle died at 10:00. Find L.

Answer: L=2.

Solution: The shorter candle lasted for 4 hours and the longer candle lasted for 6 hours. As 6 hours – 4 hours = 2 hours and 2 hours / 4 hours = 1/2, the longer candle lasted 50% longer and was, therefore, 50% longer in length. This means that the +1 in L+1 on the longer candle was 1/2 of L. 1/2L=1, so L=2*1, L=2.

Course:MATH110/Archive/2010-2011/003/Groups/Group 18

2010-11-12T05:23:47Z

RolandWill: /* 6. Three kinds of apples are all mixed up in a basket. How many apples must you draw without (without looking) from the basket to be sure of getting at least two of a kind? */

{{Infobox MATH110 Groups
| group number = 18
| member 1 = [[User:ChouJuChen|Audrey Chen]]
| member 2 = [[User:SifatHasan|Sifat Hasan]]
| member 3 = [[User:CaitlinLastiwkaFarquharson|Caitlin Lastiwka-Farquharson]]
| member 4 = [[User:VictoriaWall|Victoria Wall]]
| member 5 = [[User:RolandWill|Roland Will]]
| member 6 =
}}

==Sub-Pages==

Basic Skills Project [http://wiki.ubc.ca/Course:MATH110/003/Groups/Group_18/Basic_Skills_Project]

==Homework due October 20th, 2010==

I created a page for our homework due tomorrow: [http://wiki.ubc.ca/Course:MATH110/003/Groups/Group_18/Homework_October_20th,_2010 http://wiki.ubc.ca/Course:MATH110/003/Groups/Group 18/Homework October 20th, 2010]

-Roland

I've moved the page, it was missing the ''Course:'' part which means it was created directly inside the wiki and not as a subpage of your group page, which is something the wiki admins don't like that much. By the way, you're allowed to use spaces in the name of your pages.

-- [[User:DavidKohler|DavidKohler]] 06:28, 20 October 2010 (UTC)

1-5

Victoria Wall

1.A bus traveled from the terminal to the airport at an average speed of 30 mi/hr and the trip took an hour and 20 min. The bus then traveled from the airport back to the terminal and again averaged 30 mi/hr. However, the return trip required 80 min. Explain.

' 'Lets call the terminal T and the airport A. If the bus travelled from T to A at 30mi/hr and it took them one hour and 20 mins to get from T to A at this speed, and there are 60 minutes in one hour, it took the bus 60min + 20min to get to A which is a total of 80min. The bus took 80 min to get from T to A. To get from A to T at the same speed (30mi/hr) it took the bus 80min. 80min = 80 min. This means going from A to T or vis versa at 30 mi/hr it will take the bus 80min.

2.A lady did not have her driver's license with her when she failed to stop at a stop sign and then went three blocks down a one-way street the wrong way. A policeman saw her, but he did not stop her. Explain.

' 'The lady was walking. It never says she was driving.

3.One of three boxes contains apples, another box contains oranges, and another box contains a mixture of apples and oranges. The boxes are labeled APPLES, ORANGES and APPLES AND ORANGES, but each label is incorrect. Can you select one fruit from only one box and determine the correct labels? Explain.

' 'if you selecet from the box APPLES AND ORANGES then you will be able to see the labels if they are correct or not.

4.I am the brother of the blind fiddler, but brothers I have none. How can this be?

' 'Since it says that he is the brother of the blind fiddler it does not mean that the fiddle is male, since he has no brothers than the fiddler must be a female.

5.Two quarters rest next to each other on a table. One coin is held fixed while the second coin is rolled around the edge of the first coin with no slipping. When the moving coin returns to its original position, how many times has it revolved?

' 'This is because the moving quarters revolves two full revolutions

6-10

Caitlin Lastiwka- Farquharson

6. Three kinds of apples are all mixed up in a basket. How many apples must you draw without (without looking) from the basket to be sure of getting at least two of a kind?

' ' To be sure you are getting at least two of a kind, you must select all of the other types of apples, plus two more. Meaning that only once you have selected all of the other apples can you be sure that you will select two of the kind you desire. It can be written like this: x,a x2, b and x3, c, with x representing the quantity of apples. This can be calculated by x2 + x3 +2. X2 representing one of the types of apples, x3 representing the other type and 2 representing 2 of the kind of apples you are trying to select. This is the only way to be sure you are getting at least two of a kind. ' '

==7. Suppose you have 40 blue socks and 40 brown socks in a drawer. How many socks must you take from the drawer (without looking) to be sure of getting (i) a pair of the same colour, and (ii) a pair with different colors. ==

' 'You must take three socks from the drawer to ensure you have a pair that match. This is because if you only select two, one could be brown and one could be blue. Selecting three, ensures that at least two of them will be the same colour. As for part two, you would need to select 41 socks to ensure you had a pair of different coloured socks because if you select 40 or less you could get all the same colour, but selecting 41 ensures you will have at least one pair of mixed colour. ' '

==8. Rueben says "Two days ago I was 20 years old. Later next year I will be 23 years old." Explain how this is possible. ==

' 'It is possible if your birthday is on the 31st of December and today is the 1st of January. This is because on the 30th of December (two days ago) you we’re 20 years old and now you are 21, later this year you will turn 22 on the 31st of December, and therefore 23 the next year.' '

==9. A rope ladder hanging over the side of a boat has rungs one foot apart. Ten rungs are showing. If the tide rises five feet, how many rungs will be showing? ==

' ' 5 rungs will be showing, because if there are 10 showing now, and they are each a foot apart, then for 5 more rungs to be showing there would need to be an increase in the level of water by 5 feet. ' '

==10.Suppose one-half of all people are chocolate eaters and one-half of all people are women. (i) Does it follow that one-fourth of all people are women chocolate eaters? (ii) Does it follow that one-half of all men are chocolate eaters? Explain. ==

' ' No, it does not follow that one-fourth of all people are women chocolate eaters and it does not follow that half of all men are chocolate eaters because are completely independent scenarios. Meaning that the the amount of women there are does not influence the amount of men that will eat chocolate. For example, If 50% of people are women and 50% of the entire population including men and women eat chocolate (arrived at by using the same logic that if 1/4 of women eat chocolate and 1/4 of men eat chocolate), that entire 50% could be comprised of women, meaning that no men eat chocolate disproving the statement.

==11-14==
==Sifat Hasan==

==11 11. A woman, her older brother, her son, and her daughter are chess players. The worst player’s twin, who is one of the four players, and the best player are of opposite sex. The worst player and the best player have the same age. If this is possible, who is the worst player?==

The four players (according to age, from oldest to youngest) are: woman's older brother, woman, and the son and the daughter (of the same age). Assuming that the children are of the same age (i.e. twins), the worst player is one of them, since they are the only ones who can have a twin. Assuming that the worst player is the daughter, her brother the son, is of the opposite sex as the woman, therefore the woman is the worst player. However, since the worst and the best player are of the same age, this is not possible, because the twins are of the opposite sex and they are of different genders.

==12 A Manhattan fellow had a girlfriend in the Bronx and a girlfriend in Brooklyn. He decided which girlfriend to visit by arriving randomly at the train station and taking the first of the Bronx or Brooklyn trains that arrived. The trains to Brooklyn and the Bronx each arrived regularly every 10 minutes. Not long after he began his scheme the man's Bronx girlfriend left him because he rarely visited. Give a (logical) explanation==

Assuming that the Bronx and the Brooklyn train arrive one after the other every 10 minutes, the only logical explanation would be that the man in Manhattan coincidentally went to the station 10 minutes or less before a train to Brooklyn arrived, most of the time.

==13 If a clock takes 5 seconds to strike 5:00 (with 5 equally spaced chimes), how long does it take to strike 10:00 (with 10 equally spaced chimes)?==

If it takes 5 seconds to strike 5, there will be 4 little halts in the middle. Therefore it takes 5 chimes 4 (5/4) = 1.25 second halts to finish. For 10 chimes, there are 9 halts so, it takes 9x 1.25 = 11.25 seconds for 10 halts.

==14 One day in the maternity ward, the name tags for four girl babies became mixed up. (i) In how many different ways could two of the babies be tagged correctly and two of the babies be tagged incorrectly? (ii) In how many different ways could three of the babies be tagged correctly and one baby be tagged incorrectly?==

(i)and (ii) If we take the babies names as A,B,C and D. There are 6 different combinations of the mix up, that two babies' names can be correct and 2 can be wrong. Assuming the name tags for the babies A,B,C and D are in respective order, they are ABDC, ADCB, ACBD, DBCA, CBAD and BACD. All other combinations for example BCAD will have one correct and 3 incorrect, or all four of them correct, because if 3 are correct, the fourth one has to be correct.

==15-16==
==Roland Will==

==15. Alex says to you, “I'll bet you any amount of money that if I shuffle this deck of cards, there will always be as many red cards in the first half of the deck as there are black cards in the second half of the deck.” Should you accept his bet?==

Answer: No, you shouldn't assuming the deck has equal amounts of red and black cards as in a standard 52 card deck.
Solution: In a standard 52 card deck, half of the cards (26) are black and half are red. If you take 26 cards at random from the deck, x of them will be black and y of them will be red, and x+y=26. As there are 26 of each color in the deck, then x+?=26 for the black cards in the deck and ?+y=26 for the red cards in the deck. As x+y=26 in the first randomly selected 26 cards, then the value of black cards in the other half of the deck must equal y, and the value of red cards in the other half of the deck must equal x meaning that "there will always be as many red cards in the first half of the deck as there are black cards in the second half of the deck."

==16. Suppose that each daughter in your family has the same number of brothers as she has sisters, and each son in your family has twice as many sisters as he has brothers. How many sons and daughters are in the family?==

Answer:3 total, 2 sister and 1 brother
Solution: Since the daughters in the family each have as many brothers as sisters the amount of sisters, with x standing for the amount of brothers, is x+1. As each brother has twice as many sisters as brothers, the amount of sisters must equal 2(x-1) or 2x-2. To find the number of brother: x+1=2x+1, 1=x-2, 3=x, which means that their are 3 brothers and 4 sisters (x+1= the number of sisters and x=3). This makes sense because a sister would have an equal amount of brothers to sisters, 3 sisters and 3 brothers, if there were 4 sisters and 3 brothers total, and each brother would have 4 sisters and 3 brothers, which is twice the amount of brothers to sisters.

==17~21==
==Audrey Chen==

==17.The zero point on a bathroom scale is set incorrectly, but otherwise the scale is accurate. It shows 60 kg when Dan stands on the scale, 50 kg when Sarah stands on the scale, but 105 kg when Dan and Sarah both stand on the scale. Does the scale read too high or too low? Explain. ==

''The scale read too low, since Dan is shown as 60kg and Sarah is 50kg, suppose 60+50=110, 105-110=-5, so that means the scale is smaller than 0 in the beginning''

==18. Alice takes one-third of the pennies from a large jar. Then Bret takes one-third of the remaining pennies from the jar. Finally, Carla takes one-third of the remaining pennies from the jar, leaving 40 pennies in the jar. How many pennies were in the jar at the start? ==

''If the total pennies is "x", Alice take 1/3x, so it has 2/3x left after Alice took it, than Bret take 1/3 out, after Alice took it, which is 2/3x*1/3= 2/9x, so in the beginning they have x, after Alice took it, it has 2/3x left, and Bret took 2/9x, so after Bret took it, it becomes 2/3x-2/9x= 4/9x-2/9x=2/9x left in the jar. Than Carla take 1/3 of the rest, so she took 1/3 of rest which is 2/9x*1/3=3/27x, so Alice took 1/3x, Bret tool 2/9x, Carla took 3/27x, three of them totaly took 1/3x+2/9x+3/27x=18/27x, so there still has x-18/27x= 9/27x= 1/3 left, 1/3x=40pennies, so x=120 pennies, so it was having 120 pennies in the jar.

==19. One morning each member of Angela's family drank an eight-ounce cup of coffee and milk, with the (nonzero) amounts of coffee and milk varying from cup to cup. Angela drank a quarter of the total amount of milk and a sixth of the total amount of coffee. What is the least number of people in the family? ==

''If we let total milk is x, total coffee is y. Than 1/4x+1/6y=8, and because every cup is 8ounce, x+y is multiple by 8. So make it easier, we use 1/4x+1/6y=8 * 12 to both sides. than we will got 3x+2y=96, now we have 3x+2y=96 and x+y is multiple of 8, and the number that multiple by 8 is 8, 16, 24, 32... so 2x+2y= 16, 32, 48, 64, 80, 96, since 3x+2y=96, it can't be more than 96. It will only have 6 possible number, so if you take 3x+2y=96 substracting 2x+2y=16, 32, 48, 64, 80, 96 you can get 6 possible x, which are 80, 64, 48, 32, 16, and 0. Than put the number into 3x+2y=96, if you put 80 in, will get 20, which is bigger than 8, and also 64, 48. If we use 32, it will equal to 8, but that means we have 0 coffee, but coffee can't be 0, so there's only 16 and 0 left. Since Angela had 1/4 of total amount of milk, milk can't be 0. So we got 16ounce than 16*(1/4)=4, so that means she had 8-4=4 's coffee. So 4=1/6 coffee, than the total amount of coffee would be 4*6=24. than x=16 and y=24, 16+24=40 40/8ounce=5, so at least have 5 cups of drinks, so that means at least they have 5 members in Angela's family.''

==20.Of two clocks next to each other, one runs 5 min per hour fast and the other runs 5 min per hour slow. At midnight the clocks show the same time. At what time are they are one hour apart? ==

''Since one clock runs 5 min faster per hour, the other is 5 min slower, after clock runs an hour, two clocks will have 10 min different from each other. 60 min an hour. 60/10=6, so after 6 hours two clocks will having one hour apart, and that would be 6AM.''

==21.Sven placed exactly in the middle among all runners in a race. Dan was slower than Sven, in 10th place, and Lars was in 16th place. How many runners were in the race? ==

''There were 17 runners. Since lars was in 16th place, the runners at least have to be 16, than if Sven is placed exactly in the middle, it means it would have even number of runners. Because Dan is slower and he was at 10 place that tells us Seven has to be before 10th, and if there has 19 runners, Sven and Dan would be at the same place, so it should be 17 runners, than Sven would be at exactly in the middle which at 9th place.''

==22-25==

Roland Will

22. During a vacation, it rained on 13 days, but when it rained in the morning, the afternoon was sunny, and every rainy afternoon was preceded by a sunny morning. There were 11 sunny mornings and 12 sunny afternoons. How long was the vacation?

Answer: 18 days of vacation.

Solution: 13 of the days of vacation were half sunny and half rainy. As there were 23 sunny mornings and afternoons (11 sunny mornings+12 sunny afternoons = 23 sunny mornings and afternoons), 13 of those sunny afternoons or mornings were on half rainy days. This means there are 10 sunny half-days left over, which equal 5 sunny full days. The 5 sunny full days plus the 13 half sunny/rainy days equal 18 total days of vacation.

23. Suppose you overhear the following conversation: Paul: How old are your three children? Paula: The product of their ages is 36 and the sum of their ages is the same as today's date. Paul: That is not enough information. Paula: The oldest child also has red hair. If you were Paul could you determine the ages of Paula's children? Explain.

Answer: If I were Paul this might be possible, but since we don’t know the date that Paula said this, it is not possible for us to find out.

Solution: There are many different combinations of three numbers that can be multiplied and will produce 36. As we do not know the date that Paula said this, the only thing we can be sure of is that the sum of the ages is less than 31 because no month has more than 31 days. Unfortunately, only one set of ages (ages 1 year old, 1 year old and 36 years old) has a sum greater than 31, which leaves many possible combinations open as possible. For today’s date, the 13th, ages of 2, 2, and 9 would produce 36 and have a sum of 13, but, again, it is uncertain. If it were the first of the month, there would be no possible combinations that would produce 36 and sum 1.

24. Two candles of equal length were lit at the same time. One candle took 6 hr to burn out and the other candle took 3 hr to burn out. After how much time was one candle exactly twice as long as the other candle?

Answer: 2 hours.

Solution: The faster burning candle took half the time to burn as the slower burning candle (3 hours/ 6 hours = 1/2), meaning it burned twice as fast. This means that after 2/3 of the total burning time for the faster burning candle it will be 1/3 of its original height and at the slower burning candle will be at 2/3 of its original height and 1/3 is half of 2/3. Since the faster burning candle took 3 hours to burn, 2/3 of its total burning time is 2 hours.

25. Two candles of length L and L + 1 were lit at 6:00 and 4:30, respectively. At 8:30 they had the same length. The longer candle died at 10:30 and the shorter candle died at 10:00. Find L.

Answer: L=2.

Solution: The shorter candle lasted for 4 hours and the longer candle lasted for 6 hours. As 6 hours – 4 hours = 2 hours and 2 hours / 4 hours = 1/2, the longer candle lasted 50% longer and was, therefore, 50% longer in length. This means that the +1 in L+1 on the longer candle was 1/2 of L. 1/2L=1, so L=2*1, L=2.

Course:MATH110/Archive/2010-2011/003/Groups/Group 18

2010-11-12T05:23:37Z

RolandWill: /* Caitlin Lastiwka- Farquharson */

{{Infobox MATH110 Groups
| group number = 18
| member 1 = [[User:ChouJuChen|Audrey Chen]]
| member 2 = [[User:SifatHasan|Sifat Hasan]]
| member 3 = [[User:CaitlinLastiwkaFarquharson|Caitlin Lastiwka-Farquharson]]
| member 4 = [[User:VictoriaWall|Victoria Wall]]
| member 5 = [[User:RolandWill|Roland Will]]
| member 6 =
}}

==Sub-Pages==

Basic Skills Project [http://wiki.ubc.ca/Course:MATH110/003/Groups/Group_18/Basic_Skills_Project]

==Homework due October 20th, 2010==

I created a page for our homework due tomorrow: [http://wiki.ubc.ca/Course:MATH110/003/Groups/Group_18/Homework_October_20th,_2010 http://wiki.ubc.ca/Course:MATH110/003/Groups/Group 18/Homework October 20th, 2010]

-Roland

I've moved the page, it was missing the ''Course:'' part which means it was created directly inside the wiki and not as a subpage of your group page, which is something the wiki admins don't like that much. By the way, you're allowed to use spaces in the name of your pages.

-- [[User:DavidKohler|DavidKohler]] 06:28, 20 October 2010 (UTC)

1-5

Victoria Wall

1.A bus traveled from the terminal to the airport at an average speed of 30 mi/hr and the trip took an hour and 20 min. The bus then traveled from the airport back to the terminal and again averaged 30 mi/hr. However, the return trip required 80 min. Explain.

' 'Lets call the terminal T and the airport A. If the bus travelled from T to A at 30mi/hr and it took them one hour and 20 mins to get from T to A at this speed, and there are 60 minutes in one hour, it took the bus 60min + 20min to get to A which is a total of 80min. The bus took 80 min to get from T to A. To get from A to T at the same speed (30mi/hr) it took the bus 80min. 80min = 80 min. This means going from A to T or vis versa at 30 mi/hr it will take the bus 80min.

2.A lady did not have her driver's license with her when she failed to stop at a stop sign and then went three blocks down a one-way street the wrong way. A policeman saw her, but he did not stop her. Explain.

' 'The lady was walking. It never says she was driving.

3.One of three boxes contains apples, another box contains oranges, and another box contains a mixture of apples and oranges. The boxes are labeled APPLES, ORANGES and APPLES AND ORANGES, but each label is incorrect. Can you select one fruit from only one box and determine the correct labels? Explain.

' 'if you selecet from the box APPLES AND ORANGES then you will be able to see the labels if they are correct or not.

4.I am the brother of the blind fiddler, but brothers I have none. How can this be?

' 'Since it says that he is the brother of the blind fiddler it does not mean that the fiddle is male, since he has no brothers than the fiddler must be a female.

5.Two quarters rest next to each other on a table. One coin is held fixed while the second coin is rolled around the edge of the first coin with no slipping. When the moving coin returns to its original position, how many times has it revolved?

' 'This is because the moving quarters revolves two full revolutions

6-10

Caitlin Lastiwka- Farquharson

==6. Three kinds of apples are all mixed up in a basket. How many apples must you draw without (without looking) from the basket to be sure of getting at least two of a kind? ==

' ' To be sure you are getting at least two of a kind, you must select all of the other types of apples, plus two more. Meaning that only once you have selected all of the other apples can you be sure that you will select two of the kind you desire. It can be written like this: x,a x2, b and x3, c, with x representing the quantity of apples. This can be calculated by x2 + x3 +2. X2 representing one of the types of apples, x3 representing the other type and 2 representing 2 of the kind of apples you are trying to select. This is the only way to be sure you are getting at least two of a kind. ' '

==7. Suppose you have 40 blue socks and 40 brown socks in a drawer. How many socks must you take from the drawer (without looking) to be sure of getting (i) a pair of the same colour, and (ii) a pair with different colors. ==

' 'You must take three socks from the drawer to ensure you have a pair that match. This is because if you only select two, one could be brown and one could be blue. Selecting three, ensures that at least two of them will be the same colour. As for part two, you would need to select 41 socks to ensure you had a pair of different coloured socks because if you select 40 or less you could get all the same colour, but selecting 41 ensures you will have at least one pair of mixed colour. ' '

==8. Rueben says "Two days ago I was 20 years old. Later next year I will be 23 years old." Explain how this is possible. ==

' 'It is possible if your birthday is on the 31st of December and today is the 1st of January. This is because on the 30th of December (two days ago) you we’re 20 years old and now you are 21, later this year you will turn 22 on the 31st of December, and therefore 23 the next year.' '

==9. A rope ladder hanging over the side of a boat has rungs one foot apart. Ten rungs are showing. If the tide rises five feet, how many rungs will be showing? ==

' ' 5 rungs will be showing, because if there are 10 showing now, and they are each a foot apart, then for 5 more rungs to be showing there would need to be an increase in the level of water by 5 feet. ' '

==10.Suppose one-half of all people are chocolate eaters and one-half of all people are women. (i) Does it follow that one-fourth of all people are women chocolate eaters? (ii) Does it follow that one-half of all men are chocolate eaters? Explain. ==

' ' No, it does not follow that one-fourth of all people are women chocolate eaters and it does not follow that half of all men are chocolate eaters because are completely independent scenarios. Meaning that the the amount of women there are does not influence the amount of men that will eat chocolate. For example, If 50% of people are women and 50% of the entire population including men and women eat chocolate (arrived at by using the same logic that if 1/4 of women eat chocolate and 1/4 of men eat chocolate), that entire 50% could be comprised of women, meaning that no men eat chocolate disproving the statement.

==11-14==
==Sifat Hasan==

==11 11. A woman, her older brother, her son, and her daughter are chess players. The worst player’s twin, who is one of the four players, and the best player are of opposite sex. The worst player and the best player have the same age. If this is possible, who is the worst player?==

The four players (according to age, from oldest to youngest) are: woman's older brother, woman, and the son and the daughter (of the same age). Assuming that the children are of the same age (i.e. twins), the worst player is one of them, since they are the only ones who can have a twin. Assuming that the worst player is the daughter, her brother the son, is of the opposite sex as the woman, therefore the woman is the worst player. However, since the worst and the best player are of the same age, this is not possible, because the twins are of the opposite sex and they are of different genders.

==12 A Manhattan fellow had a girlfriend in the Bronx and a girlfriend in Brooklyn. He decided which girlfriend to visit by arriving randomly at the train station and taking the first of the Bronx or Brooklyn trains that arrived. The trains to Brooklyn and the Bronx each arrived regularly every 10 minutes. Not long after he began his scheme the man's Bronx girlfriend left him because he rarely visited. Give a (logical) explanation==

Assuming that the Bronx and the Brooklyn train arrive one after the other every 10 minutes, the only logical explanation would be that the man in Manhattan coincidentally went to the station 10 minutes or less before a train to Brooklyn arrived, most of the time.

==13 If a clock takes 5 seconds to strike 5:00 (with 5 equally spaced chimes), how long does it take to strike 10:00 (with 10 equally spaced chimes)?==

If it takes 5 seconds to strike 5, there will be 4 little halts in the middle. Therefore it takes 5 chimes 4 (5/4) = 1.25 second halts to finish. For 10 chimes, there are 9 halts so, it takes 9x 1.25 = 11.25 seconds for 10 halts.

==14 One day in the maternity ward, the name tags for four girl babies became mixed up. (i) In how many different ways could two of the babies be tagged correctly and two of the babies be tagged incorrectly? (ii) In how many different ways could three of the babies be tagged correctly and one baby be tagged incorrectly?==

(i)and (ii) If we take the babies names as A,B,C and D. There are 6 different combinations of the mix up, that two babies' names can be correct and 2 can be wrong. Assuming the name tags for the babies A,B,C and D are in respective order, they are ABDC, ADCB, ACBD, DBCA, CBAD and BACD. All other combinations for example BCAD will have one correct and 3 incorrect, or all four of them correct, because if 3 are correct, the fourth one has to be correct.

==15-16==
==Roland Will==

==15. Alex says to you, “I'll bet you any amount of money that if I shuffle this deck of cards, there will always be as many red cards in the first half of the deck as there are black cards in the second half of the deck.” Should you accept his bet?==

Answer: No, you shouldn't assuming the deck has equal amounts of red and black cards as in a standard 52 card deck.
Solution: In a standard 52 card deck, half of the cards (26) are black and half are red. If you take 26 cards at random from the deck, x of them will be black and y of them will be red, and x+y=26. As there are 26 of each color in the deck, then x+?=26 for the black cards in the deck and ?+y=26 for the red cards in the deck. As x+y=26 in the first randomly selected 26 cards, then the value of black cards in the other half of the deck must equal y, and the value of red cards in the other half of the deck must equal x meaning that "there will always be as many red cards in the first half of the deck as there are black cards in the second half of the deck."

==16. Suppose that each daughter in your family has the same number of brothers as she has sisters, and each son in your family has twice as many sisters as he has brothers. How many sons and daughters are in the family?==

Answer:3 total, 2 sister and 1 brother
Solution: Since the daughters in the family each have as many brothers as sisters the amount of sisters, with x standing for the amount of brothers, is x+1. As each brother has twice as many sisters as brothers, the amount of sisters must equal 2(x-1) or 2x-2. To find the number of brother: x+1=2x+1, 1=x-2, 3=x, which means that their are 3 brothers and 4 sisters (x+1= the number of sisters and x=3). This makes sense because a sister would have an equal amount of brothers to sisters, 3 sisters and 3 brothers, if there were 4 sisters and 3 brothers total, and each brother would have 4 sisters and 3 brothers, which is twice the amount of brothers to sisters.

==17~21==
==Audrey Chen==

==17.The zero point on a bathroom scale is set incorrectly, but otherwise the scale is accurate. It shows 60 kg when Dan stands on the scale, 50 kg when Sarah stands on the scale, but 105 kg when Dan and Sarah both stand on the scale. Does the scale read too high or too low? Explain. ==

''The scale read too low, since Dan is shown as 60kg and Sarah is 50kg, suppose 60+50=110, 105-110=-5, so that means the scale is smaller than 0 in the beginning''

==18. Alice takes one-third of the pennies from a large jar. Then Bret takes one-third of the remaining pennies from the jar. Finally, Carla takes one-third of the remaining pennies from the jar, leaving 40 pennies in the jar. How many pennies were in the jar at the start? ==

''If the total pennies is "x", Alice take 1/3x, so it has 2/3x left after Alice took it, than Bret take 1/3 out, after Alice took it, which is 2/3x*1/3= 2/9x, so in the beginning they have x, after Alice took it, it has 2/3x left, and Bret took 2/9x, so after Bret took it, it becomes 2/3x-2/9x= 4/9x-2/9x=2/9x left in the jar. Than Carla take 1/3 of the rest, so she took 1/3 of rest which is 2/9x*1/3=3/27x, so Alice took 1/3x, Bret tool 2/9x, Carla took 3/27x, three of them totaly took 1/3x+2/9x+3/27x=18/27x, so there still has x-18/27x= 9/27x= 1/3 left, 1/3x=40pennies, so x=120 pennies, so it was having 120 pennies in the jar.

==19. One morning each member of Angela's family drank an eight-ounce cup of coffee and milk, with the (nonzero) amounts of coffee and milk varying from cup to cup. Angela drank a quarter of the total amount of milk and a sixth of the total amount of coffee. What is the least number of people in the family? ==

''If we let total milk is x, total coffee is y. Than 1/4x+1/6y=8, and because every cup is 8ounce, x+y is multiple by 8. So make it easier, we use 1/4x+1/6y=8 * 12 to both sides. than we will got 3x+2y=96, now we have 3x+2y=96 and x+y is multiple of 8, and the number that multiple by 8 is 8, 16, 24, 32... so 2x+2y= 16, 32, 48, 64, 80, 96, since 3x+2y=96, it can't be more than 96. It will only have 6 possible number, so if you take 3x+2y=96 substracting 2x+2y=16, 32, 48, 64, 80, 96 you can get 6 possible x, which are 80, 64, 48, 32, 16, and 0. Than put the number into 3x+2y=96, if you put 80 in, will get 20, which is bigger than 8, and also 64, 48. If we use 32, it will equal to 8, but that means we have 0 coffee, but coffee can't be 0, so there's only 16 and 0 left. Since Angela had 1/4 of total amount of milk, milk can't be 0. So we got 16ounce than 16*(1/4)=4, so that means she had 8-4=4 's coffee. So 4=1/6 coffee, than the total amount of coffee would be 4*6=24. than x=16 and y=24, 16+24=40 40/8ounce=5, so at least have 5 cups of drinks, so that means at least they have 5 members in Angela's family.''

==20.Of two clocks next to each other, one runs 5 min per hour fast and the other runs 5 min per hour slow. At midnight the clocks show the same time. At what time are they are one hour apart? ==

''Since one clock runs 5 min faster per hour, the other is 5 min slower, after clock runs an hour, two clocks will have 10 min different from each other. 60 min an hour. 60/10=6, so after 6 hours two clocks will having one hour apart, and that would be 6AM.''

==21.Sven placed exactly in the middle among all runners in a race. Dan was slower than Sven, in 10th place, and Lars was in 16th place. How many runners were in the race? ==

''There were 17 runners. Since lars was in 16th place, the runners at least have to be 16, than if Sven is placed exactly in the middle, it means it would have even number of runners. Because Dan is slower and he was at 10 place that tells us Seven has to be before 10th, and if there has 19 runners, Sven and Dan would be at the same place, so it should be 17 runners, than Sven would be at exactly in the middle which at 9th place.''

==22-25==

Roland Will

22. During a vacation, it rained on 13 days, but when it rained in the morning, the afternoon was sunny, and every rainy afternoon was preceded by a sunny morning. There were 11 sunny mornings and 12 sunny afternoons. How long was the vacation?

Answer: 18 days of vacation.

Solution: 13 of the days of vacation were half sunny and half rainy. As there were 23 sunny mornings and afternoons (11 sunny mornings+12 sunny afternoons = 23 sunny mornings and afternoons), 13 of those sunny afternoons or mornings were on half rainy days. This means there are 10 sunny half-days left over, which equal 5 sunny full days. The 5 sunny full days plus the 13 half sunny/rainy days equal 18 total days of vacation.

23. Suppose you overhear the following conversation: Paul: How old are your three children? Paula: The product of their ages is 36 and the sum of their ages is the same as today's date. Paul: That is not enough information. Paula: The oldest child also has red hair. If you were Paul could you determine the ages of Paula's children? Explain.

Answer: If I were Paul this might be possible, but since we don’t know the date that Paula said this, it is not possible for us to find out.

Solution: There are many different combinations of three numbers that can be multiplied and will produce 36. As we do not know the date that Paula said this, the only thing we can be sure of is that the sum of the ages is less than 31 because no month has more than 31 days. Unfortunately, only one set of ages (ages 1 year old, 1 year old and 36 years old) has a sum greater than 31, which leaves many possible combinations open as possible. For today’s date, the 13th, ages of 2, 2, and 9 would produce 36 and have a sum of 13, but, again, it is uncertain. If it were the first of the month, there would be no possible combinations that would produce 36 and sum 1.

24. Two candles of equal length were lit at the same time. One candle took 6 hr to burn out and the other candle took 3 hr to burn out. After how much time was one candle exactly twice as long as the other candle?

Answer: 2 hours.

Solution: The faster burning candle took half the time to burn as the slower burning candle (3 hours/ 6 hours = 1/2), meaning it burned twice as fast. This means that after 2/3 of the total burning time for the faster burning candle it will be 1/3 of its original height and at the slower burning candle will be at 2/3 of its original height and 1/3 is half of 2/3. Since the faster burning candle took 3 hours to burn, 2/3 of its total burning time is 2 hours.

25. Two candles of length L and L + 1 were lit at 6:00 and 4:30, respectively. At 8:30 they had the same length. The longer candle died at 10:30 and the shorter candle died at 10:00. Find L.

Answer: L=2.

Solution: The shorter candle lasted for 4 hours and the longer candle lasted for 6 hours. As 6 hours – 4 hours = 2 hours and 2 hours / 4 hours = 1/2, the longer candle lasted 50% longer and was, therefore, 50% longer in length. This means that the +1 in L+1 on the longer candle was 1/2 of L. 1/2L=1, so L=2*1, L=2.

Course:MATH110/Archive/2010-2011/003/Groups/Group 18

2010-11-12T05:23:28Z

RolandWill: /* 6-10 */

{{Infobox MATH110 Groups
| group number = 18
| member 1 = [[User:ChouJuChen|Audrey Chen]]
| member 2 = [[User:SifatHasan|Sifat Hasan]]
| member 3 = [[User:CaitlinLastiwkaFarquharson|Caitlin Lastiwka-Farquharson]]
| member 4 = [[User:VictoriaWall|Victoria Wall]]
| member 5 = [[User:RolandWill|Roland Will]]
| member 6 =
}}

==Sub-Pages==

Basic Skills Project [http://wiki.ubc.ca/Course:MATH110/003/Groups/Group_18/Basic_Skills_Project]

==Homework due October 20th, 2010==

I created a page for our homework due tomorrow: [http://wiki.ubc.ca/Course:MATH110/003/Groups/Group_18/Homework_October_20th,_2010 http://wiki.ubc.ca/Course:MATH110/003/Groups/Group 18/Homework October 20th, 2010]

-Roland

I've moved the page, it was missing the ''Course:'' part which means it was created directly inside the wiki and not as a subpage of your group page, which is something the wiki admins don't like that much. By the way, you're allowed to use spaces in the name of your pages.

-- [[User:DavidKohler|DavidKohler]] 06:28, 20 October 2010 (UTC)

1-5

Victoria Wall

1.A bus traveled from the terminal to the airport at an average speed of 30 mi/hr and the trip took an hour and 20 min. The bus then traveled from the airport back to the terminal and again averaged 30 mi/hr. However, the return trip required 80 min. Explain.

' 'Lets call the terminal T and the airport A. If the bus travelled from T to A at 30mi/hr and it took them one hour and 20 mins to get from T to A at this speed, and there are 60 minutes in one hour, it took the bus 60min + 20min to get to A which is a total of 80min. The bus took 80 min to get from T to A. To get from A to T at the same speed (30mi/hr) it took the bus 80min. 80min = 80 min. This means going from A to T or vis versa at 30 mi/hr it will take the bus 80min.

2.A lady did not have her driver's license with her when she failed to stop at a stop sign and then went three blocks down a one-way street the wrong way. A policeman saw her, but he did not stop her. Explain.

' 'The lady was walking. It never says she was driving.

3.One of three boxes contains apples, another box contains oranges, and another box contains a mixture of apples and oranges. The boxes are labeled APPLES, ORANGES and APPLES AND ORANGES, but each label is incorrect. Can you select one fruit from only one box and determine the correct labels? Explain.

' 'if you selecet from the box APPLES AND ORANGES then you will be able to see the labels if they are correct or not.

4.I am the brother of the blind fiddler, but brothers I have none. How can this be?

' 'Since it says that he is the brother of the blind fiddler it does not mean that the fiddle is male, since he has no brothers than the fiddler must be a female.

5.Two quarters rest next to each other on a table. One coin is held fixed while the second coin is rolled around the edge of the first coin with no slipping. When the moving coin returns to its original position, how many times has it revolved?

' 'This is because the moving quarters revolves two full revolutions

6-10

== Caitlin Lastiwka- Farquharson ==

==6. Three kinds of apples are all mixed up in a basket. How many apples must you draw without (without looking) from the basket to be sure of getting at least two of a kind? ==

' ' To be sure you are getting at least two of a kind, you must select all of the other types of apples, plus two more. Meaning that only once you have selected all of the other apples can you be sure that you will select two of the kind you desire. It can be written like this: x,a x2, b and x3, c, with x representing the quantity of apples. This can be calculated by x2 + x3 +2. X2 representing one of the types of apples, x3 representing the other type and 2 representing 2 of the kind of apples you are trying to select. This is the only way to be sure you are getting at least two of a kind. ' '

==7. Suppose you have 40 blue socks and 40 brown socks in a drawer. How many socks must you take from the drawer (without looking) to be sure of getting (i) a pair of the same colour, and (ii) a pair with different colors. ==

' 'You must take three socks from the drawer to ensure you have a pair that match. This is because if you only select two, one could be brown and one could be blue. Selecting three, ensures that at least two of them will be the same colour. As for part two, you would need to select 41 socks to ensure you had a pair of different coloured socks because if you select 40 or less you could get all the same colour, but selecting 41 ensures you will have at least one pair of mixed colour. ' '

==8. Rueben says "Two days ago I was 20 years old. Later next year I will be 23 years old." Explain how this is possible. ==

' 'It is possible if your birthday is on the 31st of December and today is the 1st of January. This is because on the 30th of December (two days ago) you we’re 20 years old and now you are 21, later this year you will turn 22 on the 31st of December, and therefore 23 the next year.' '

==9. A rope ladder hanging over the side of a boat has rungs one foot apart. Ten rungs are showing. If the tide rises five feet, how many rungs will be showing? ==

' ' 5 rungs will be showing, because if there are 10 showing now, and they are each a foot apart, then for 5 more rungs to be showing there would need to be an increase in the level of water by 5 feet. ' '

==10.Suppose one-half of all people are chocolate eaters and one-half of all people are women. (i) Does it follow that one-fourth of all people are women chocolate eaters? (ii) Does it follow that one-half of all men are chocolate eaters? Explain. ==

' ' No, it does not follow that one-fourth of all people are women chocolate eaters and it does not follow that half of all men are chocolate eaters because are completely independent scenarios. Meaning that the the amount of women there are does not influence the amount of men that will eat chocolate. For example, If 50% of people are women and 50% of the entire population including men and women eat chocolate (arrived at by using the same logic that if 1/4 of women eat chocolate and 1/4 of men eat chocolate), that entire 50% could be comprised of women, meaning that no men eat chocolate disproving the statement.

==11-14==
==Sifat Hasan==

==11 11. A woman, her older brother, her son, and her daughter are chess players. The worst player’s twin, who is one of the four players, and the best player are of opposite sex. The worst player and the best player have the same age. If this is possible, who is the worst player?==

The four players (according to age, from oldest to youngest) are: woman's older brother, woman, and the son and the daughter (of the same age). Assuming that the children are of the same age (i.e. twins), the worst player is one of them, since they are the only ones who can have a twin. Assuming that the worst player is the daughter, her brother the son, is of the opposite sex as the woman, therefore the woman is the worst player. However, since the worst and the best player are of the same age, this is not possible, because the twins are of the opposite sex and they are of different genders.

==12 A Manhattan fellow had a girlfriend in the Bronx and a girlfriend in Brooklyn. He decided which girlfriend to visit by arriving randomly at the train station and taking the first of the Bronx or Brooklyn trains that arrived. The trains to Brooklyn and the Bronx each arrived regularly every 10 minutes. Not long after he began his scheme the man's Bronx girlfriend left him because he rarely visited. Give a (logical) explanation==

Assuming that the Bronx and the Brooklyn train arrive one after the other every 10 minutes, the only logical explanation would be that the man in Manhattan coincidentally went to the station 10 minutes or less before a train to Brooklyn arrived, most of the time.

==13 If a clock takes 5 seconds to strike 5:00 (with 5 equally spaced chimes), how long does it take to strike 10:00 (with 10 equally spaced chimes)?==

If it takes 5 seconds to strike 5, there will be 4 little halts in the middle. Therefore it takes 5 chimes 4 (5/4) = 1.25 second halts to finish. For 10 chimes, there are 9 halts so, it takes 9x 1.25 = 11.25 seconds for 10 halts.

==14 One day in the maternity ward, the name tags for four girl babies became mixed up. (i) In how many different ways could two of the babies be tagged correctly and two of the babies be tagged incorrectly? (ii) In how many different ways could three of the babies be tagged correctly and one baby be tagged incorrectly?==

(i)and (ii) If we take the babies names as A,B,C and D. There are 6 different combinations of the mix up, that two babies' names can be correct and 2 can be wrong. Assuming the name tags for the babies A,B,C and D are in respective order, they are ABDC, ADCB, ACBD, DBCA, CBAD and BACD. All other combinations for example BCAD will have one correct and 3 incorrect, or all four of them correct, because if 3 are correct, the fourth one has to be correct.

==15-16==
==Roland Will==

==15. Alex says to you, “I'll bet you any amount of money that if I shuffle this deck of cards, there will always be as many red cards in the first half of the deck as there are black cards in the second half of the deck.” Should you accept his bet?==

Answer: No, you shouldn't assuming the deck has equal amounts of red and black cards as in a standard 52 card deck.
Solution: In a standard 52 card deck, half of the cards (26) are black and half are red. If you take 26 cards at random from the deck, x of them will be black and y of them will be red, and x+y=26. As there are 26 of each color in the deck, then x+?=26 for the black cards in the deck and ?+y=26 for the red cards in the deck. As x+y=26 in the first randomly selected 26 cards, then the value of black cards in the other half of the deck must equal y, and the value of red cards in the other half of the deck must equal x meaning that "there will always be as many red cards in the first half of the deck as there are black cards in the second half of the deck."

==16. Suppose that each daughter in your family has the same number of brothers as she has sisters, and each son in your family has twice as many sisters as he has brothers. How many sons and daughters are in the family?==

Answer:3 total, 2 sister and 1 brother
Solution: Since the daughters in the family each have as many brothers as sisters the amount of sisters, with x standing for the amount of brothers, is x+1. As each brother has twice as many sisters as brothers, the amount of sisters must equal 2(x-1) or 2x-2. To find the number of brother: x+1=2x+1, 1=x-2, 3=x, which means that their are 3 brothers and 4 sisters (x+1= the number of sisters and x=3). This makes sense because a sister would have an equal amount of brothers to sisters, 3 sisters and 3 brothers, if there were 4 sisters and 3 brothers total, and each brother would have 4 sisters and 3 brothers, which is twice the amount of brothers to sisters.

==17~21==
==Audrey Chen==

==17.The zero point on a bathroom scale is set incorrectly, but otherwise the scale is accurate. It shows 60 kg when Dan stands on the scale, 50 kg when Sarah stands on the scale, but 105 kg when Dan and Sarah both stand on the scale. Does the scale read too high or too low? Explain. ==

''The scale read too low, since Dan is shown as 60kg and Sarah is 50kg, suppose 60+50=110, 105-110=-5, so that means the scale is smaller than 0 in the beginning''

==18. Alice takes one-third of the pennies from a large jar. Then Bret takes one-third of the remaining pennies from the jar. Finally, Carla takes one-third of the remaining pennies from the jar, leaving 40 pennies in the jar. How many pennies were in the jar at the start? ==

''If the total pennies is "x", Alice take 1/3x, so it has 2/3x left after Alice took it, than Bret take 1/3 out, after Alice took it, which is 2/3x*1/3= 2/9x, so in the beginning they have x, after Alice took it, it has 2/3x left, and Bret took 2/9x, so after Bret took it, it becomes 2/3x-2/9x= 4/9x-2/9x=2/9x left in the jar. Than Carla take 1/3 of the rest, so she took 1/3 of rest which is 2/9x*1/3=3/27x, so Alice took 1/3x, Bret tool 2/9x, Carla took 3/27x, three of them totaly took 1/3x+2/9x+3/27x=18/27x, so there still has x-18/27x= 9/27x= 1/3 left, 1/3x=40pennies, so x=120 pennies, so it was having 120 pennies in the jar.

==19. One morning each member of Angela's family drank an eight-ounce cup of coffee and milk, with the (nonzero) amounts of coffee and milk varying from cup to cup. Angela drank a quarter of the total amount of milk and a sixth of the total amount of coffee. What is the least number of people in the family? ==

''If we let total milk is x, total coffee is y. Than 1/4x+1/6y=8, and because every cup is 8ounce, x+y is multiple by 8. So make it easier, we use 1/4x+1/6y=8 * 12 to both sides. than we will got 3x+2y=96, now we have 3x+2y=96 and x+y is multiple of 8, and the number that multiple by 8 is 8, 16, 24, 32... so 2x+2y= 16, 32, 48, 64, 80, 96, since 3x+2y=96, it can't be more than 96. It will only have 6 possible number, so if you take 3x+2y=96 substracting 2x+2y=16, 32, 48, 64, 80, 96 you can get 6 possible x, which are 80, 64, 48, 32, 16, and 0. Than put the number into 3x+2y=96, if you put 80 in, will get 20, which is bigger than 8, and also 64, 48. If we use 32, it will equal to 8, but that means we have 0 coffee, but coffee can't be 0, so there's only 16 and 0 left. Since Angela had 1/4 of total amount of milk, milk can't be 0. So we got 16ounce than 16*(1/4)=4, so that means she had 8-4=4 's coffee. So 4=1/6 coffee, than the total amount of coffee would be 4*6=24. than x=16 and y=24, 16+24=40 40/8ounce=5, so at least have 5 cups of drinks, so that means at least they have 5 members in Angela's family.''

==20.Of two clocks next to each other, one runs 5 min per hour fast and the other runs 5 min per hour slow. At midnight the clocks show the same time. At what time are they are one hour apart? ==

''Since one clock runs 5 min faster per hour, the other is 5 min slower, after clock runs an hour, two clocks will have 10 min different from each other. 60 min an hour. 60/10=6, so after 6 hours two clocks will having one hour apart, and that would be 6AM.''

==21.Sven placed exactly in the middle among all runners in a race. Dan was slower than Sven, in 10th place, and Lars was in 16th place. How many runners were in the race? ==

''There were 17 runners. Since lars was in 16th place, the runners at least have to be 16, than if Sven is placed exactly in the middle, it means it would have even number of runners. Because Dan is slower and he was at 10 place that tells us Seven has to be before 10th, and if there has 19 runners, Sven and Dan would be at the same place, so it should be 17 runners, than Sven would be at exactly in the middle which at 9th place.''

==22-25==

Roland Will

22. During a vacation, it rained on 13 days, but when it rained in the morning, the afternoon was sunny, and every rainy afternoon was preceded by a sunny morning. There were 11 sunny mornings and 12 sunny afternoons. How long was the vacation?

Answer: 18 days of vacation.

Solution: 13 of the days of vacation were half sunny and half rainy. As there were 23 sunny mornings and afternoons (11 sunny mornings+12 sunny afternoons = 23 sunny mornings and afternoons), 13 of those sunny afternoons or mornings were on half rainy days. This means there are 10 sunny half-days left over, which equal 5 sunny full days. The 5 sunny full days plus the 13 half sunny/rainy days equal 18 total days of vacation.

23. Suppose you overhear the following conversation: Paul: How old are your three children? Paula: The product of their ages is 36 and the sum of their ages is the same as today's date. Paul: That is not enough information. Paula: The oldest child also has red hair. If you were Paul could you determine the ages of Paula's children? Explain.

Answer: If I were Paul this might be possible, but since we don’t know the date that Paula said this, it is not possible for us to find out.

Solution: There are many different combinations of three numbers that can be multiplied and will produce 36. As we do not know the date that Paula said this, the only thing we can be sure of is that the sum of the ages is less than 31 because no month has more than 31 days. Unfortunately, only one set of ages (ages 1 year old, 1 year old and 36 years old) has a sum greater than 31, which leaves many possible combinations open as possible. For today’s date, the 13th, ages of 2, 2, and 9 would produce 36 and have a sum of 13, but, again, it is uncertain. If it were the first of the month, there would be no possible combinations that would produce 36 and sum 1.

24. Two candles of equal length were lit at the same time. One candle took 6 hr to burn out and the other candle took 3 hr to burn out. After how much time was one candle exactly twice as long as the other candle?

Answer: 2 hours.

Solution: The faster burning candle took half the time to burn as the slower burning candle (3 hours/ 6 hours = 1/2), meaning it burned twice as fast. This means that after 2/3 of the total burning time for the faster burning candle it will be 1/3 of its original height and at the slower burning candle will be at 2/3 of its original height and 1/3 is half of 2/3. Since the faster burning candle took 3 hours to burn, 2/3 of its total burning time is 2 hours.

25. Two candles of length L and L + 1 were lit at 6:00 and 4:30, respectively. At 8:30 they had the same length. The longer candle died at 10:30 and the shorter candle died at 10:00. Find L.

Answer: L=2.

Solution: The shorter candle lasted for 4 hours and the longer candle lasted for 6 hours. As 6 hours – 4 hours = 2 hours and 2 hours / 4 hours = 1/2, the longer candle lasted 50% longer and was, therefore, 50% longer in length. This means that the +1 in L+1 on the longer candle was 1/2 of L. 1/2L=1, so L=2*1, L=2.

Course:MATH110/Archive/2010-2011/003/Groups/Group 18

2010-11-12T05:23:16Z

RolandWill: /* 5.Two quarters rest next to each other on a table. One coin is held fixed while the second coin is rolled around the edge of the first coin with no slipping. When the moving coin returns to its original position, how many times has it revolved? */

{{Infobox MATH110 Groups
| group number = 18
| member 1 = [[User:ChouJuChen|Audrey Chen]]
| member 2 = [[User:SifatHasan|Sifat Hasan]]
| member 3 = [[User:CaitlinLastiwkaFarquharson|Caitlin Lastiwka-Farquharson]]
| member 4 = [[User:VictoriaWall|Victoria Wall]]
| member 5 = [[User:RolandWill|Roland Will]]
| member 6 =
}}

==Sub-Pages==

Basic Skills Project [http://wiki.ubc.ca/Course:MATH110/003/Groups/Group_18/Basic_Skills_Project]

==Homework due October 20th, 2010==

I created a page for our homework due tomorrow: [http://wiki.ubc.ca/Course:MATH110/003/Groups/Group_18/Homework_October_20th,_2010 http://wiki.ubc.ca/Course:MATH110/003/Groups/Group 18/Homework October 20th, 2010]

-Roland

I've moved the page, it was missing the ''Course:'' part which means it was created directly inside the wiki and not as a subpage of your group page, which is something the wiki admins don't like that much. By the way, you're allowed to use spaces in the name of your pages.

-- [[User:DavidKohler|DavidKohler]] 06:28, 20 October 2010 (UTC)

1-5

Victoria Wall

1.A bus traveled from the terminal to the airport at an average speed of 30 mi/hr and the trip took an hour and 20 min. The bus then traveled from the airport back to the terminal and again averaged 30 mi/hr. However, the return trip required 80 min. Explain.

' 'Lets call the terminal T and the airport A. If the bus travelled from T to A at 30mi/hr and it took them one hour and 20 mins to get from T to A at this speed, and there are 60 minutes in one hour, it took the bus 60min + 20min to get to A which is a total of 80min. The bus took 80 min to get from T to A. To get from A to T at the same speed (30mi/hr) it took the bus 80min. 80min = 80 min. This means going from A to T or vis versa at 30 mi/hr it will take the bus 80min.

2.A lady did not have her driver's license with her when she failed to stop at a stop sign and then went three blocks down a one-way street the wrong way. A policeman saw her, but he did not stop her. Explain.

' 'The lady was walking. It never says she was driving.

3.One of three boxes contains apples, another box contains oranges, and another box contains a mixture of apples and oranges. The boxes are labeled APPLES, ORANGES and APPLES AND ORANGES, but each label is incorrect. Can you select one fruit from only one box and determine the correct labels? Explain.

' 'if you selecet from the box APPLES AND ORANGES then you will be able to see the labels if they are correct or not.

4.I am the brother of the blind fiddler, but brothers I have none. How can this be?

' 'Since it says that he is the brother of the blind fiddler it does not mean that the fiddle is male, since he has no brothers than the fiddler must be a female.

5.Two quarters rest next to each other on a table. One coin is held fixed while the second coin is rolled around the edge of the first coin with no slipping. When the moving coin returns to its original position, how many times has it revolved?

' 'This is because the moving quarters revolves two full revolutions

==6-10==
== Caitlin Lastiwka- Farquharson ==

==6. Three kinds of apples are all mixed up in a basket. How many apples must you draw without (without looking) from the basket to be sure of getting at least two of a kind? ==

' ' To be sure you are getting at least two of a kind, you must select all of the other types of apples, plus two more. Meaning that only once you have selected all of the other apples can you be sure that you will select two of the kind you desire. It can be written like this: x,a x2, b and x3, c, with x representing the quantity of apples. This can be calculated by x2 + x3 +2. X2 representing one of the types of apples, x3 representing the other type and 2 representing 2 of the kind of apples you are trying to select. This is the only way to be sure you are getting at least two of a kind. ' '

==7. Suppose you have 40 blue socks and 40 brown socks in a drawer. How many socks must you take from the drawer (without looking) to be sure of getting (i) a pair of the same colour, and (ii) a pair with different colors. ==

' 'You must take three socks from the drawer to ensure you have a pair that match. This is because if you only select two, one could be brown and one could be blue. Selecting three, ensures that at least two of them will be the same colour. As for part two, you would need to select 41 socks to ensure you had a pair of different coloured socks because if you select 40 or less you could get all the same colour, but selecting 41 ensures you will have at least one pair of mixed colour. ' '

==8. Rueben says "Two days ago I was 20 years old. Later next year I will be 23 years old." Explain how this is possible. ==

' 'It is possible if your birthday is on the 31st of December and today is the 1st of January. This is because on the 30th of December (two days ago) you we’re 20 years old and now you are 21, later this year you will turn 22 on the 31st of December, and therefore 23 the next year.' '

==9. A rope ladder hanging over the side of a boat has rungs one foot apart. Ten rungs are showing. If the tide rises five feet, how many rungs will be showing? ==

' ' 5 rungs will be showing, because if there are 10 showing now, and they are each a foot apart, then for 5 more rungs to be showing there would need to be an increase in the level of water by 5 feet. ' '

==10.Suppose one-half of all people are chocolate eaters and one-half of all people are women. (i) Does it follow that one-fourth of all people are women chocolate eaters? (ii) Does it follow that one-half of all men are chocolate eaters? Explain. ==

' ' No, it does not follow that one-fourth of all people are women chocolate eaters and it does not follow that half of all men are chocolate eaters because are completely independent scenarios. Meaning that the the amount of women there are does not influence the amount of men that will eat chocolate. For example, If 50% of people are women and 50% of the entire population including men and women eat chocolate (arrived at by using the same logic that if 1/4 of women eat chocolate and 1/4 of men eat chocolate), that entire 50% could be comprised of women, meaning that no men eat chocolate disproving the statement.

==11-14==
==Sifat Hasan==

==11 11. A woman, her older brother, her son, and her daughter are chess players. The worst player’s twin, who is one of the four players, and the best player are of opposite sex. The worst player and the best player have the same age. If this is possible, who is the worst player?==

The four players (according to age, from oldest to youngest) are: woman's older brother, woman, and the son and the daughter (of the same age). Assuming that the children are of the same age (i.e. twins), the worst player is one of them, since they are the only ones who can have a twin. Assuming that the worst player is the daughter, her brother the son, is of the opposite sex as the woman, therefore the woman is the worst player. However, since the worst and the best player are of the same age, this is not possible, because the twins are of the opposite sex and they are of different genders.

==12 A Manhattan fellow had a girlfriend in the Bronx and a girlfriend in Brooklyn. He decided which girlfriend to visit by arriving randomly at the train station and taking the first of the Bronx or Brooklyn trains that arrived. The trains to Brooklyn and the Bronx each arrived regularly every 10 minutes. Not long after he began his scheme the man's Bronx girlfriend left him because he rarely visited. Give a (logical) explanation==

Assuming that the Bronx and the Brooklyn train arrive one after the other every 10 minutes, the only logical explanation would be that the man in Manhattan coincidentally went to the station 10 minutes or less before a train to Brooklyn arrived, most of the time.

==13 If a clock takes 5 seconds to strike 5:00 (with 5 equally spaced chimes), how long does it take to strike 10:00 (with 10 equally spaced chimes)?==

If it takes 5 seconds to strike 5, there will be 4 little halts in the middle. Therefore it takes 5 chimes 4 (5/4) = 1.25 second halts to finish. For 10 chimes, there are 9 halts so, it takes 9x 1.25 = 11.25 seconds for 10 halts.

==14 One day in the maternity ward, the name tags for four girl babies became mixed up. (i) In how many different ways could two of the babies be tagged correctly and two of the babies be tagged incorrectly? (ii) In how many different ways could three of the babies be tagged correctly and one baby be tagged incorrectly?==

(i)and (ii) If we take the babies names as A,B,C and D. There are 6 different combinations of the mix up, that two babies' names can be correct and 2 can be wrong. Assuming the name tags for the babies A,B,C and D are in respective order, they are ABDC, ADCB, ACBD, DBCA, CBAD and BACD. All other combinations for example BCAD will have one correct and 3 incorrect, or all four of them correct, because if 3 are correct, the fourth one has to be correct.

==15-16==
==Roland Will==

==15. Alex says to you, “I'll bet you any amount of money that if I shuffle this deck of cards, there will always be as many red cards in the first half of the deck as there are black cards in the second half of the deck.” Should you accept his bet?==

Answer: No, you shouldn't assuming the deck has equal amounts of red and black cards as in a standard 52 card deck.
Solution: In a standard 52 card deck, half of the cards (26) are black and half are red. If you take 26 cards at random from the deck, x of them will be black and y of them will be red, and x+y=26. As there are 26 of each color in the deck, then x+?=26 for the black cards in the deck and ?+y=26 for the red cards in the deck. As x+y=26 in the first randomly selected 26 cards, then the value of black cards in the other half of the deck must equal y, and the value of red cards in the other half of the deck must equal x meaning that "there will always be as many red cards in the first half of the deck as there are black cards in the second half of the deck."

==16. Suppose that each daughter in your family has the same number of brothers as she has sisters, and each son in your family has twice as many sisters as he has brothers. How many sons and daughters are in the family?==

Answer:3 total, 2 sister and 1 brother
Solution: Since the daughters in the family each have as many brothers as sisters the amount of sisters, with x standing for the amount of brothers, is x+1. As each brother has twice as many sisters as brothers, the amount of sisters must equal 2(x-1) or 2x-2. To find the number of brother: x+1=2x+1, 1=x-2, 3=x, which means that their are 3 brothers and 4 sisters (x+1= the number of sisters and x=3). This makes sense because a sister would have an equal amount of brothers to sisters, 3 sisters and 3 brothers, if there were 4 sisters and 3 brothers total, and each brother would have 4 sisters and 3 brothers, which is twice the amount of brothers to sisters.

==17~21==
==Audrey Chen==

==17.The zero point on a bathroom scale is set incorrectly, but otherwise the scale is accurate. It shows 60 kg when Dan stands on the scale, 50 kg when Sarah stands on the scale, but 105 kg when Dan and Sarah both stand on the scale. Does the scale read too high or too low? Explain. ==

''The scale read too low, since Dan is shown as 60kg and Sarah is 50kg, suppose 60+50=110, 105-110=-5, so that means the scale is smaller than 0 in the beginning''

==18. Alice takes one-third of the pennies from a large jar. Then Bret takes one-third of the remaining pennies from the jar. Finally, Carla takes one-third of the remaining pennies from the jar, leaving 40 pennies in the jar. How many pennies were in the jar at the start? ==

''If the total pennies is "x", Alice take 1/3x, so it has 2/3x left after Alice took it, than Bret take 1/3 out, after Alice took it, which is 2/3x*1/3= 2/9x, so in the beginning they have x, after Alice took it, it has 2/3x left, and Bret took 2/9x, so after Bret took it, it becomes 2/3x-2/9x= 4/9x-2/9x=2/9x left in the jar. Than Carla take 1/3 of the rest, so she took 1/3 of rest which is 2/9x*1/3=3/27x, so Alice took 1/3x, Bret tool 2/9x, Carla took 3/27x, three of them totaly took 1/3x+2/9x+3/27x=18/27x, so there still has x-18/27x= 9/27x= 1/3 left, 1/3x=40pennies, so x=120 pennies, so it was having 120 pennies in the jar.

==19. One morning each member of Angela's family drank an eight-ounce cup of coffee and milk, with the (nonzero) amounts of coffee and milk varying from cup to cup. Angela drank a quarter of the total amount of milk and a sixth of the total amount of coffee. What is the least number of people in the family? ==

''If we let total milk is x, total coffee is y. Than 1/4x+1/6y=8, and because every cup is 8ounce, x+y is multiple by 8. So make it easier, we use 1/4x+1/6y=8 * 12 to both sides. than we will got 3x+2y=96, now we have 3x+2y=96 and x+y is multiple of 8, and the number that multiple by 8 is 8, 16, 24, 32... so 2x+2y= 16, 32, 48, 64, 80, 96, since 3x+2y=96, it can't be more than 96. It will only have 6 possible number, so if you take 3x+2y=96 substracting 2x+2y=16, 32, 48, 64, 80, 96 you can get 6 possible x, which are 80, 64, 48, 32, 16, and 0. Than put the number into 3x+2y=96, if you put 80 in, will get 20, which is bigger than 8, and also 64, 48. If we use 32, it will equal to 8, but that means we have 0 coffee, but coffee can't be 0, so there's only 16 and 0 left. Since Angela had 1/4 of total amount of milk, milk can't be 0. So we got 16ounce than 16*(1/4)=4, so that means she had 8-4=4 's coffee. So 4=1/6 coffee, than the total amount of coffee would be 4*6=24. than x=16 and y=24, 16+24=40 40/8ounce=5, so at least have 5 cups of drinks, so that means at least they have 5 members in Angela's family.''

==20.Of two clocks next to each other, one runs 5 min per hour fast and the other runs 5 min per hour slow. At midnight the clocks show the same time. At what time are they are one hour apart? ==

''Since one clock runs 5 min faster per hour, the other is 5 min slower, after clock runs an hour, two clocks will have 10 min different from each other. 60 min an hour. 60/10=6, so after 6 hours two clocks will having one hour apart, and that would be 6AM.''

==21.Sven placed exactly in the middle among all runners in a race. Dan was slower than Sven, in 10th place, and Lars was in 16th place. How many runners were in the race? ==

''There were 17 runners. Since lars was in 16th place, the runners at least have to be 16, than if Sven is placed exactly in the middle, it means it would have even number of runners. Because Dan is slower and he was at 10 place that tells us Seven has to be before 10th, and if there has 19 runners, Sven and Dan would be at the same place, so it should be 17 runners, than Sven would be at exactly in the middle which at 9th place.''

==22-25==

Roland Will

22. During a vacation, it rained on 13 days, but when it rained in the morning, the afternoon was sunny, and every rainy afternoon was preceded by a sunny morning. There were 11 sunny mornings and 12 sunny afternoons. How long was the vacation?

Answer: 18 days of vacation.

Solution: 13 of the days of vacation were half sunny and half rainy. As there were 23 sunny mornings and afternoons (11 sunny mornings+12 sunny afternoons = 23 sunny mornings and afternoons), 13 of those sunny afternoons or mornings were on half rainy days. This means there are 10 sunny half-days left over, which equal 5 sunny full days. The 5 sunny full days plus the 13 half sunny/rainy days equal 18 total days of vacation.

23. Suppose you overhear the following conversation: Paul: How old are your three children? Paula: The product of their ages is 36 and the sum of their ages is the same as today's date. Paul: That is not enough information. Paula: The oldest child also has red hair. If you were Paul could you determine the ages of Paula's children? Explain.

Answer: If I were Paul this might be possible, but since we don’t know the date that Paula said this, it is not possible for us to find out.

Solution: There are many different combinations of three numbers that can be multiplied and will produce 36. As we do not know the date that Paula said this, the only thing we can be sure of is that the sum of the ages is less than 31 because no month has more than 31 days. Unfortunately, only one set of ages (ages 1 year old, 1 year old and 36 years old) has a sum greater than 31, which leaves many possible combinations open as possible. For today’s date, the 13th, ages of 2, 2, and 9 would produce 36 and have a sum of 13, but, again, it is uncertain. If it were the first of the month, there would be no possible combinations that would produce 36 and sum 1.

24. Two candles of equal length were lit at the same time. One candle took 6 hr to burn out and the other candle took 3 hr to burn out. After how much time was one candle exactly twice as long as the other candle?

Answer: 2 hours.

Solution: The faster burning candle took half the time to burn as the slower burning candle (3 hours/ 6 hours = 1/2), meaning it burned twice as fast. This means that after 2/3 of the total burning time for the faster burning candle it will be 1/3 of its original height and at the slower burning candle will be at 2/3 of its original height and 1/3 is half of 2/3. Since the faster burning candle took 3 hours to burn, 2/3 of its total burning time is 2 hours.

25. Two candles of length L and L + 1 were lit at 6:00 and 4:30, respectively. At 8:30 they had the same length. The longer candle died at 10:30 and the shorter candle died at 10:00. Find L.

Answer: L=2.

Solution: The shorter candle lasted for 4 hours and the longer candle lasted for 6 hours. As 6 hours – 4 hours = 2 hours and 2 hours / 4 hours = 1/2, the longer candle lasted 50% longer and was, therefore, 50% longer in length. This means that the +1 in L+1 on the longer candle was 1/2 of L. 1/2L=1, so L=2*1, L=2.

Course:MATH110/Archive/2010-2011/003/Groups/Group 18

2010-11-12T05:22:59Z

RolandWill: /* 4.I am the brother of the blind fiddler, but brothers I have none. How can this be? */

{{Infobox MATH110 Groups
| group number = 18
| member 1 = [[User:ChouJuChen|Audrey Chen]]
| member 2 = [[User:SifatHasan|Sifat Hasan]]
| member 3 = [[User:CaitlinLastiwkaFarquharson|Caitlin Lastiwka-Farquharson]]
| member 4 = [[User:VictoriaWall|Victoria Wall]]
| member 5 = [[User:RolandWill|Roland Will]]
| member 6 =
}}

==Sub-Pages==

Basic Skills Project [http://wiki.ubc.ca/Course:MATH110/003/Groups/Group_18/Basic_Skills_Project]

==Homework due October 20th, 2010==

I created a page for our homework due tomorrow: [http://wiki.ubc.ca/Course:MATH110/003/Groups/Group_18/Homework_October_20th,_2010 http://wiki.ubc.ca/Course:MATH110/003/Groups/Group 18/Homework October 20th, 2010]

-Roland

I've moved the page, it was missing the ''Course:'' part which means it was created directly inside the wiki and not as a subpage of your group page, which is something the wiki admins don't like that much. By the way, you're allowed to use spaces in the name of your pages.

-- [[User:DavidKohler|DavidKohler]] 06:28, 20 October 2010 (UTC)

1-5

Victoria Wall

1.A bus traveled from the terminal to the airport at an average speed of 30 mi/hr and the trip took an hour and 20 min. The bus then traveled from the airport back to the terminal and again averaged 30 mi/hr. However, the return trip required 80 min. Explain.

' 'Lets call the terminal T and the airport A. If the bus travelled from T to A at 30mi/hr and it took them one hour and 20 mins to get from T to A at this speed, and there are 60 minutes in one hour, it took the bus 60min + 20min to get to A which is a total of 80min. The bus took 80 min to get from T to A. To get from A to T at the same speed (30mi/hr) it took the bus 80min. 80min = 80 min. This means going from A to T or vis versa at 30 mi/hr it will take the bus 80min.

2.A lady did not have her driver's license with her when she failed to stop at a stop sign and then went three blocks down a one-way street the wrong way. A policeman saw her, but he did not stop her. Explain.

' 'The lady was walking. It never says she was driving.

3.One of three boxes contains apples, another box contains oranges, and another box contains a mixture of apples and oranges. The boxes are labeled APPLES, ORANGES and APPLES AND ORANGES, but each label is incorrect. Can you select one fruit from only one box and determine the correct labels? Explain.

' 'if you selecet from the box APPLES AND ORANGES then you will be able to see the labels if they are correct or not.

4.I am the brother of the blind fiddler, but brothers I have none. How can this be?

' 'Since it says that he is the brother of the blind fiddler it does not mean that the fiddle is male, since he has no brothers than the fiddler must be a female.

==5.Two quarters rest next to each other on a table. One coin is held fixed while the second coin is rolled around the edge of the first coin with no slipping. When the moving coin returns to its original position, how many times has it revolved? ==

' 'This is because the moving quarters revolves two full revolutions

==6-10==
== Caitlin Lastiwka- Farquharson ==

==6. Three kinds of apples are all mixed up in a basket. How many apples must you draw without (without looking) from the basket to be sure of getting at least two of a kind? ==

' ' To be sure you are getting at least two of a kind, you must select all of the other types of apples, plus two more. Meaning that only once you have selected all of the other apples can you be sure that you will select two of the kind you desire. It can be written like this: x,a x2, b and x3, c, with x representing the quantity of apples. This can be calculated by x2 + x3 +2. X2 representing one of the types of apples, x3 representing the other type and 2 representing 2 of the kind of apples you are trying to select. This is the only way to be sure you are getting at least two of a kind. ' '

==7. Suppose you have 40 blue socks and 40 brown socks in a drawer. How many socks must you take from the drawer (without looking) to be sure of getting (i) a pair of the same colour, and (ii) a pair with different colors. ==

' 'You must take three socks from the drawer to ensure you have a pair that match. This is because if you only select two, one could be brown and one could be blue. Selecting three, ensures that at least two of them will be the same colour. As for part two, you would need to select 41 socks to ensure you had a pair of different coloured socks because if you select 40 or less you could get all the same colour, but selecting 41 ensures you will have at least one pair of mixed colour. ' '

==8. Rueben says "Two days ago I was 20 years old. Later next year I will be 23 years old." Explain how this is possible. ==

' 'It is possible if your birthday is on the 31st of December and today is the 1st of January. This is because on the 30th of December (two days ago) you we’re 20 years old and now you are 21, later this year you will turn 22 on the 31st of December, and therefore 23 the next year.' '

==9. A rope ladder hanging over the side of a boat has rungs one foot apart. Ten rungs are showing. If the tide rises five feet, how many rungs will be showing? ==

' ' 5 rungs will be showing, because if there are 10 showing now, and they are each a foot apart, then for 5 more rungs to be showing there would need to be an increase in the level of water by 5 feet. ' '

==10.Suppose one-half of all people are chocolate eaters and one-half of all people are women. (i) Does it follow that one-fourth of all people are women chocolate eaters? (ii) Does it follow that one-half of all men are chocolate eaters? Explain. ==

' ' No, it does not follow that one-fourth of all people are women chocolate eaters and it does not follow that half of all men are chocolate eaters because are completely independent scenarios. Meaning that the the amount of women there are does not influence the amount of men that will eat chocolate. For example, If 50% of people are women and 50% of the entire population including men and women eat chocolate (arrived at by using the same logic that if 1/4 of women eat chocolate and 1/4 of men eat chocolate), that entire 50% could be comprised of women, meaning that no men eat chocolate disproving the statement.

==11-14==
==Sifat Hasan==

==11 11. A woman, her older brother, her son, and her daughter are chess players. The worst player’s twin, who is one of the four players, and the best player are of opposite sex. The worst player and the best player have the same age. If this is possible, who is the worst player?==

The four players (according to age, from oldest to youngest) are: woman's older brother, woman, and the son and the daughter (of the same age). Assuming that the children are of the same age (i.e. twins), the worst player is one of them, since they are the only ones who can have a twin. Assuming that the worst player is the daughter, her brother the son, is of the opposite sex as the woman, therefore the woman is the worst player. However, since the worst and the best player are of the same age, this is not possible, because the twins are of the opposite sex and they are of different genders.

==12 A Manhattan fellow had a girlfriend in the Bronx and a girlfriend in Brooklyn. He decided which girlfriend to visit by arriving randomly at the train station and taking the first of the Bronx or Brooklyn trains that arrived. The trains to Brooklyn and the Bronx each arrived regularly every 10 minutes. Not long after he began his scheme the man's Bronx girlfriend left him because he rarely visited. Give a (logical) explanation==

Assuming that the Bronx and the Brooklyn train arrive one after the other every 10 minutes, the only logical explanation would be that the man in Manhattan coincidentally went to the station 10 minutes or less before a train to Brooklyn arrived, most of the time.

==13 If a clock takes 5 seconds to strike 5:00 (with 5 equally spaced chimes), how long does it take to strike 10:00 (with 10 equally spaced chimes)?==

If it takes 5 seconds to strike 5, there will be 4 little halts in the middle. Therefore it takes 5 chimes 4 (5/4) = 1.25 second halts to finish. For 10 chimes, there are 9 halts so, it takes 9x 1.25 = 11.25 seconds for 10 halts.

==14 One day in the maternity ward, the name tags for four girl babies became mixed up. (i) In how many different ways could two of the babies be tagged correctly and two of the babies be tagged incorrectly? (ii) In how many different ways could three of the babies be tagged correctly and one baby be tagged incorrectly?==

(i)and (ii) If we take the babies names as A,B,C and D. There are 6 different combinations of the mix up, that two babies' names can be correct and 2 can be wrong. Assuming the name tags for the babies A,B,C and D are in respective order, they are ABDC, ADCB, ACBD, DBCA, CBAD and BACD. All other combinations for example BCAD will have one correct and 3 incorrect, or all four of them correct, because if 3 are correct, the fourth one has to be correct.

==15-16==
==Roland Will==

==15. Alex says to you, “I'll bet you any amount of money that if I shuffle this deck of cards, there will always be as many red cards in the first half of the deck as there are black cards in the second half of the deck.” Should you accept his bet?==

Answer: No, you shouldn't assuming the deck has equal amounts of red and black cards as in a standard 52 card deck.
Solution: In a standard 52 card deck, half of the cards (26) are black and half are red. If you take 26 cards at random from the deck, x of them will be black and y of them will be red, and x+y=26. As there are 26 of each color in the deck, then x+?=26 for the black cards in the deck and ?+y=26 for the red cards in the deck. As x+y=26 in the first randomly selected 26 cards, then the value of black cards in the other half of the deck must equal y, and the value of red cards in the other half of the deck must equal x meaning that "there will always be as many red cards in the first half of the deck as there are black cards in the second half of the deck."

==16. Suppose that each daughter in your family has the same number of brothers as she has sisters, and each son in your family has twice as many sisters as he has brothers. How many sons and daughters are in the family?==

Answer:3 total, 2 sister and 1 brother
Solution: Since the daughters in the family each have as many brothers as sisters the amount of sisters, with x standing for the amount of brothers, is x+1. As each brother has twice as many sisters as brothers, the amount of sisters must equal 2(x-1) or 2x-2. To find the number of brother: x+1=2x+1, 1=x-2, 3=x, which means that their are 3 brothers and 4 sisters (x+1= the number of sisters and x=3). This makes sense because a sister would have an equal amount of brothers to sisters, 3 sisters and 3 brothers, if there were 4 sisters and 3 brothers total, and each brother would have 4 sisters and 3 brothers, which is twice the amount of brothers to sisters.

==17~21==
==Audrey Chen==

==17.The zero point on a bathroom scale is set incorrectly, but otherwise the scale is accurate. It shows 60 kg when Dan stands on the scale, 50 kg when Sarah stands on the scale, but 105 kg when Dan and Sarah both stand on the scale. Does the scale read too high or too low? Explain. ==

''The scale read too low, since Dan is shown as 60kg and Sarah is 50kg, suppose 60+50=110, 105-110=-5, so that means the scale is smaller than 0 in the beginning''

==18. Alice takes one-third of the pennies from a large jar. Then Bret takes one-third of the remaining pennies from the jar. Finally, Carla takes one-third of the remaining pennies from the jar, leaving 40 pennies in the jar. How many pennies were in the jar at the start? ==

''If the total pennies is "x", Alice take 1/3x, so it has 2/3x left after Alice took it, than Bret take 1/3 out, after Alice took it, which is 2/3x*1/3= 2/9x, so in the beginning they have x, after Alice took it, it has 2/3x left, and Bret took 2/9x, so after Bret took it, it becomes 2/3x-2/9x= 4/9x-2/9x=2/9x left in the jar. Than Carla take 1/3 of the rest, so she took 1/3 of rest which is 2/9x*1/3=3/27x, so Alice took 1/3x, Bret tool 2/9x, Carla took 3/27x, three of them totaly took 1/3x+2/9x+3/27x=18/27x, so there still has x-18/27x= 9/27x= 1/3 left, 1/3x=40pennies, so x=120 pennies, so it was having 120 pennies in the jar.

==19. One morning each member of Angela's family drank an eight-ounce cup of coffee and milk, with the (nonzero) amounts of coffee and milk varying from cup to cup. Angela drank a quarter of the total amount of milk and a sixth of the total amount of coffee. What is the least number of people in the family? ==

''If we let total milk is x, total coffee is y. Than 1/4x+1/6y=8, and because every cup is 8ounce, x+y is multiple by 8. So make it easier, we use 1/4x+1/6y=8 * 12 to both sides. than we will got 3x+2y=96, now we have 3x+2y=96 and x+y is multiple of 8, and the number that multiple by 8 is 8, 16, 24, 32... so 2x+2y= 16, 32, 48, 64, 80, 96, since 3x+2y=96, it can't be more than 96. It will only have 6 possible number, so if you take 3x+2y=96 substracting 2x+2y=16, 32, 48, 64, 80, 96 you can get 6 possible x, which are 80, 64, 48, 32, 16, and 0. Than put the number into 3x+2y=96, if you put 80 in, will get 20, which is bigger than 8, and also 64, 48. If we use 32, it will equal to 8, but that means we have 0 coffee, but coffee can't be 0, so there's only 16 and 0 left. Since Angela had 1/4 of total amount of milk, milk can't be 0. So we got 16ounce than 16*(1/4)=4, so that means she had 8-4=4 's coffee. So 4=1/6 coffee, than the total amount of coffee would be 4*6=24. than x=16 and y=24, 16+24=40 40/8ounce=5, so at least have 5 cups of drinks, so that means at least they have 5 members in Angela's family.''

==20.Of two clocks next to each other, one runs 5 min per hour fast and the other runs 5 min per hour slow. At midnight the clocks show the same time. At what time are they are one hour apart? ==

''Since one clock runs 5 min faster per hour, the other is 5 min slower, after clock runs an hour, two clocks will have 10 min different from each other. 60 min an hour. 60/10=6, so after 6 hours two clocks will having one hour apart, and that would be 6AM.''

==21.Sven placed exactly in the middle among all runners in a race. Dan was slower than Sven, in 10th place, and Lars was in 16th place. How many runners were in the race? ==

''There were 17 runners. Since lars was in 16th place, the runners at least have to be 16, than if Sven is placed exactly in the middle, it means it would have even number of runners. Because Dan is slower and he was at 10 place that tells us Seven has to be before 10th, and if there has 19 runners, Sven and Dan would be at the same place, so it should be 17 runners, than Sven would be at exactly in the middle which at 9th place.''

==22-25==

Roland Will

22. During a vacation, it rained on 13 days, but when it rained in the morning, the afternoon was sunny, and every rainy afternoon was preceded by a sunny morning. There were 11 sunny mornings and 12 sunny afternoons. How long was the vacation?

Answer: 18 days of vacation.

Solution: 13 of the days of vacation were half sunny and half rainy. As there were 23 sunny mornings and afternoons (11 sunny mornings+12 sunny afternoons = 23 sunny mornings and afternoons), 13 of those sunny afternoons or mornings were on half rainy days. This means there are 10 sunny half-days left over, which equal 5 sunny full days. The 5 sunny full days plus the 13 half sunny/rainy days equal 18 total days of vacation.

23. Suppose you overhear the following conversation: Paul: How old are your three children? Paula: The product of their ages is 36 and the sum of their ages is the same as today's date. Paul: That is not enough information. Paula: The oldest child also has red hair. If you were Paul could you determine the ages of Paula's children? Explain.

Answer: If I were Paul this might be possible, but since we don’t know the date that Paula said this, it is not possible for us to find out.

Solution: There are many different combinations of three numbers that can be multiplied and will produce 36. As we do not know the date that Paula said this, the only thing we can be sure of is that the sum of the ages is less than 31 because no month has more than 31 days. Unfortunately, only one set of ages (ages 1 year old, 1 year old and 36 years old) has a sum greater than 31, which leaves many possible combinations open as possible. For today’s date, the 13th, ages of 2, 2, and 9 would produce 36 and have a sum of 13, but, again, it is uncertain. If it were the first of the month, there would be no possible combinations that would produce 36 and sum 1.

24. Two candles of equal length were lit at the same time. One candle took 6 hr to burn out and the other candle took 3 hr to burn out. After how much time was one candle exactly twice as long as the other candle?

Answer: 2 hours.

Solution: The faster burning candle took half the time to burn as the slower burning candle (3 hours/ 6 hours = 1/2), meaning it burned twice as fast. This means that after 2/3 of the total burning time for the faster burning candle it will be 1/3 of its original height and at the slower burning candle will be at 2/3 of its original height and 1/3 is half of 2/3. Since the faster burning candle took 3 hours to burn, 2/3 of its total burning time is 2 hours.

25. Two candles of length L and L + 1 were lit at 6:00 and 4:30, respectively. At 8:30 they had the same length. The longer candle died at 10:30 and the shorter candle died at 10:00. Find L.

Answer: L=2.

Solution: The shorter candle lasted for 4 hours and the longer candle lasted for 6 hours. As 6 hours – 4 hours = 2 hours and 2 hours / 4 hours = 1/2, the longer candle lasted 50% longer and was, therefore, 50% longer in length. This means that the +1 in L+1 on the longer candle was 1/2 of L. 1/2L=1, so L=2*1, L=2.

Course:MATH110/Archive/2010-2011/003/Groups/Group 18

2010-11-12T05:22:34Z

RolandWill: /* 3.One of three boxes contains apples, another box contains oranges, and another box contains a mixture of apples and oranges. The boxes are labeled APPLES, ORANGES and APPLES AND ORANGES, but each label is incorrect. Can you select one fruit from

{{Infobox MATH110 Groups
| group number = 18
| member 1 = [[User:ChouJuChen|Audrey Chen]]
| member 2 = [[User:SifatHasan|Sifat Hasan]]
| member 3 = [[User:CaitlinLastiwkaFarquharson|Caitlin Lastiwka-Farquharson]]
| member 4 = [[User:VictoriaWall|Victoria Wall]]
| member 5 = [[User:RolandWill|Roland Will]]
| member 6 =
}}

==Sub-Pages==

Basic Skills Project [http://wiki.ubc.ca/Course:MATH110/003/Groups/Group_18/Basic_Skills_Project]

==Homework due October 20th, 2010==

I created a page for our homework due tomorrow: [http://wiki.ubc.ca/Course:MATH110/003/Groups/Group_18/Homework_October_20th,_2010 http://wiki.ubc.ca/Course:MATH110/003/Groups/Group 18/Homework October 20th, 2010]

-Roland

I've moved the page, it was missing the ''Course:'' part which means it was created directly inside the wiki and not as a subpage of your group page, which is something the wiki admins don't like that much. By the way, you're allowed to use spaces in the name of your pages.

-- [[User:DavidKohler|DavidKohler]] 06:28, 20 October 2010 (UTC)

1-5

Victoria Wall

1.A bus traveled from the terminal to the airport at an average speed of 30 mi/hr and the trip took an hour and 20 min. The bus then traveled from the airport back to the terminal and again averaged 30 mi/hr. However, the return trip required 80 min. Explain.

' 'Lets call the terminal T and the airport A. If the bus travelled from T to A at 30mi/hr and it took them one hour and 20 mins to get from T to A at this speed, and there are 60 minutes in one hour, it took the bus 60min + 20min to get to A which is a total of 80min. The bus took 80 min to get from T to A. To get from A to T at the same speed (30mi/hr) it took the bus 80min. 80min = 80 min. This means going from A to T or vis versa at 30 mi/hr it will take the bus 80min.

2.A lady did not have her driver's license with her when she failed to stop at a stop sign and then went three blocks down a one-way street the wrong way. A policeman saw her, but he did not stop her. Explain.

' 'The lady was walking. It never says she was driving.

3.One of three boxes contains apples, another box contains oranges, and another box contains a mixture of apples and oranges. The boxes are labeled APPLES, ORANGES and APPLES AND ORANGES, but each label is incorrect. Can you select one fruit from only one box and determine the correct labels? Explain.

' 'if you selecet from the box APPLES AND ORANGES then you will be able to see the labels if they are correct or not.

==4.I am the brother of the blind fiddler, but brothers I have none. How can this be? ==

' 'Since it says that he is the brother of the blind fiddler it does not mean that the fiddle is male, since he has no brothers than the fiddler must be a female.

==5.Two quarters rest next to each other on a table. One coin is held fixed while the second coin is rolled around the edge of the first coin with no slipping. When the moving coin returns to its original position, how many times has it revolved? ==

' 'This is because the moving quarters revolves two full revolutions

==6-10==
== Caitlin Lastiwka- Farquharson ==

==6. Three kinds of apples are all mixed up in a basket. How many apples must you draw without (without looking) from the basket to be sure of getting at least two of a kind? ==

' ' To be sure you are getting at least two of a kind, you must select all of the other types of apples, plus two more. Meaning that only once you have selected all of the other apples can you be sure that you will select two of the kind you desire. It can be written like this: x,a x2, b and x3, c, with x representing the quantity of apples. This can be calculated by x2 + x3 +2. X2 representing one of the types of apples, x3 representing the other type and 2 representing 2 of the kind of apples you are trying to select. This is the only way to be sure you are getting at least two of a kind. ' '

==7. Suppose you have 40 blue socks and 40 brown socks in a drawer. How many socks must you take from the drawer (without looking) to be sure of getting (i) a pair of the same colour, and (ii) a pair with different colors. ==

' 'You must take three socks from the drawer to ensure you have a pair that match. This is because if you only select two, one could be brown and one could be blue. Selecting three, ensures that at least two of them will be the same colour. As for part two, you would need to select 41 socks to ensure you had a pair of different coloured socks because if you select 40 or less you could get all the same colour, but selecting 41 ensures you will have at least one pair of mixed colour. ' '

==8. Rueben says "Two days ago I was 20 years old. Later next year I will be 23 years old." Explain how this is possible. ==

' 'It is possible if your birthday is on the 31st of December and today is the 1st of January. This is because on the 30th of December (two days ago) you we’re 20 years old and now you are 21, later this year you will turn 22 on the 31st of December, and therefore 23 the next year.' '

==9. A rope ladder hanging over the side of a boat has rungs one foot apart. Ten rungs are showing. If the tide rises five feet, how many rungs will be showing? ==

' ' 5 rungs will be showing, because if there are 10 showing now, and they are each a foot apart, then for 5 more rungs to be showing there would need to be an increase in the level of water by 5 feet. ' '

==10.Suppose one-half of all people are chocolate eaters and one-half of all people are women. (i) Does it follow that one-fourth of all people are women chocolate eaters? (ii) Does it follow that one-half of all men are chocolate eaters? Explain. ==

' ' No, it does not follow that one-fourth of all people are women chocolate eaters and it does not follow that half of all men are chocolate eaters because are completely independent scenarios. Meaning that the the amount of women there are does not influence the amount of men that will eat chocolate. For example, If 50% of people are women and 50% of the entire population including men and women eat chocolate (arrived at by using the same logic that if 1/4 of women eat chocolate and 1/4 of men eat chocolate), that entire 50% could be comprised of women, meaning that no men eat chocolate disproving the statement.

==11-14==
==Sifat Hasan==

==11 11. A woman, her older brother, her son, and her daughter are chess players. The worst player’s twin, who is one of the four players, and the best player are of opposite sex. The worst player and the best player have the same age. If this is possible, who is the worst player?==

The four players (according to age, from oldest to youngest) are: woman's older brother, woman, and the son and the daughter (of the same age). Assuming that the children are of the same age (i.e. twins), the worst player is one of them, since they are the only ones who can have a twin. Assuming that the worst player is the daughter, her brother the son, is of the opposite sex as the woman, therefore the woman is the worst player. However, since the worst and the best player are of the same age, this is not possible, because the twins are of the opposite sex and they are of different genders.

==12 A Manhattan fellow had a girlfriend in the Bronx and a girlfriend in Brooklyn. He decided which girlfriend to visit by arriving randomly at the train station and taking the first of the Bronx or Brooklyn trains that arrived. The trains to Brooklyn and the Bronx each arrived regularly every 10 minutes. Not long after he began his scheme the man's Bronx girlfriend left him because he rarely visited. Give a (logical) explanation==

Assuming that the Bronx and the Brooklyn train arrive one after the other every 10 minutes, the only logical explanation would be that the man in Manhattan coincidentally went to the station 10 minutes or less before a train to Brooklyn arrived, most of the time.

==13 If a clock takes 5 seconds to strike 5:00 (with 5 equally spaced chimes), how long does it take to strike 10:00 (with 10 equally spaced chimes)?==

If it takes 5 seconds to strike 5, there will be 4 little halts in the middle. Therefore it takes 5 chimes 4 (5/4) = 1.25 second halts to finish. For 10 chimes, there are 9 halts so, it takes 9x 1.25 = 11.25 seconds for 10 halts.

==14 One day in the maternity ward, the name tags for four girl babies became mixed up. (i) In how many different ways could two of the babies be tagged correctly and two of the babies be tagged incorrectly? (ii) In how many different ways could three of the babies be tagged correctly and one baby be tagged incorrectly?==

(i)and (ii) If we take the babies names as A,B,C and D. There are 6 different combinations of the mix up, that two babies' names can be correct and 2 can be wrong. Assuming the name tags for the babies A,B,C and D are in respective order, they are ABDC, ADCB, ACBD, DBCA, CBAD and BACD. All other combinations for example BCAD will have one correct and 3 incorrect, or all four of them correct, because if 3 are correct, the fourth one has to be correct.

==15-16==
==Roland Will==

==15. Alex says to you, “I'll bet you any amount of money that if I shuffle this deck of cards, there will always be as many red cards in the first half of the deck as there are black cards in the second half of the deck.” Should you accept his bet?==

Answer: No, you shouldn't assuming the deck has equal amounts of red and black cards as in a standard 52 card deck.
Solution: In a standard 52 card deck, half of the cards (26) are black and half are red. If you take 26 cards at random from the deck, x of them will be black and y of them will be red, and x+y=26. As there are 26 of each color in the deck, then x+?=26 for the black cards in the deck and ?+y=26 for the red cards in the deck. As x+y=26 in the first randomly selected 26 cards, then the value of black cards in the other half of the deck must equal y, and the value of red cards in the other half of the deck must equal x meaning that "there will always be as many red cards in the first half of the deck as there are black cards in the second half of the deck."

==16. Suppose that each daughter in your family has the same number of brothers as she has sisters, and each son in your family has twice as many sisters as he has brothers. How many sons and daughters are in the family?==

Answer:3 total, 2 sister and 1 brother
Solution: Since the daughters in the family each have as many brothers as sisters the amount of sisters, with x standing for the amount of brothers, is x+1. As each brother has twice as many sisters as brothers, the amount of sisters must equal 2(x-1) or 2x-2. To find the number of brother: x+1=2x+1, 1=x-2, 3=x, which means that their are 3 brothers and 4 sisters (x+1= the number of sisters and x=3). This makes sense because a sister would have an equal amount of brothers to sisters, 3 sisters and 3 brothers, if there were 4 sisters and 3 brothers total, and each brother would have 4 sisters and 3 brothers, which is twice the amount of brothers to sisters.

==17~21==
==Audrey Chen==

==17.The zero point on a bathroom scale is set incorrectly, but otherwise the scale is accurate. It shows 60 kg when Dan stands on the scale, 50 kg when Sarah stands on the scale, but 105 kg when Dan and Sarah both stand on the scale. Does the scale read too high or too low? Explain. ==

''The scale read too low, since Dan is shown as 60kg and Sarah is 50kg, suppose 60+50=110, 105-110=-5, so that means the scale is smaller than 0 in the beginning''

==18. Alice takes one-third of the pennies from a large jar. Then Bret takes one-third of the remaining pennies from the jar. Finally, Carla takes one-third of the remaining pennies from the jar, leaving 40 pennies in the jar. How many pennies were in the jar at the start? ==

''If the total pennies is "x", Alice take 1/3x, so it has 2/3x left after Alice took it, than Bret take 1/3 out, after Alice took it, which is 2/3x*1/3= 2/9x, so in the beginning they have x, after Alice took it, it has 2/3x left, and Bret took 2/9x, so after Bret took it, it becomes 2/3x-2/9x= 4/9x-2/9x=2/9x left in the jar. Than Carla take 1/3 of the rest, so she took 1/3 of rest which is 2/9x*1/3=3/27x, so Alice took 1/3x, Bret tool 2/9x, Carla took 3/27x, three of them totaly took 1/3x+2/9x+3/27x=18/27x, so there still has x-18/27x= 9/27x= 1/3 left, 1/3x=40pennies, so x=120 pennies, so it was having 120 pennies in the jar.

==19. One morning each member of Angela's family drank an eight-ounce cup of coffee and milk, with the (nonzero) amounts of coffee and milk varying from cup to cup. Angela drank a quarter of the total amount of milk and a sixth of the total amount of coffee. What is the least number of people in the family? ==

''If we let total milk is x, total coffee is y. Than 1/4x+1/6y=8, and because every cup is 8ounce, x+y is multiple by 8. So make it easier, we use 1/4x+1/6y=8 * 12 to both sides. than we will got 3x+2y=96, now we have 3x+2y=96 and x+y is multiple of 8, and the number that multiple by 8 is 8, 16, 24, 32... so 2x+2y= 16, 32, 48, 64, 80, 96, since 3x+2y=96, it can't be more than 96. It will only have 6 possible number, so if you take 3x+2y=96 substracting 2x+2y=16, 32, 48, 64, 80, 96 you can get 6 possible x, which are 80, 64, 48, 32, 16, and 0. Than put the number into 3x+2y=96, if you put 80 in, will get 20, which is bigger than 8, and also 64, 48. If we use 32, it will equal to 8, but that means we have 0 coffee, but coffee can't be 0, so there's only 16 and 0 left. Since Angela had 1/4 of total amount of milk, milk can't be 0. So we got 16ounce than 16*(1/4)=4, so that means she had 8-4=4 's coffee. So 4=1/6 coffee, than the total amount of coffee would be 4*6=24. than x=16 and y=24, 16+24=40 40/8ounce=5, so at least have 5 cups of drinks, so that means at least they have 5 members in Angela's family.''

==20.Of two clocks next to each other, one runs 5 min per hour fast and the other runs 5 min per hour slow. At midnight the clocks show the same time. At what time are they are one hour apart? ==

''Since one clock runs 5 min faster per hour, the other is 5 min slower, after clock runs an hour, two clocks will have 10 min different from each other. 60 min an hour. 60/10=6, so after 6 hours two clocks will having one hour apart, and that would be 6AM.''

==21.Sven placed exactly in the middle among all runners in a race. Dan was slower than Sven, in 10th place, and Lars was in 16th place. How many runners were in the race? ==

''There were 17 runners. Since lars was in 16th place, the runners at least have to be 16, than if Sven is placed exactly in the middle, it means it would have even number of runners. Because Dan is slower and he was at 10 place that tells us Seven has to be before 10th, and if there has 19 runners, Sven and Dan would be at the same place, so it should be 17 runners, than Sven would be at exactly in the middle which at 9th place.''

==22-25==

Roland Will

22. During a vacation, it rained on 13 days, but when it rained in the morning, the afternoon was sunny, and every rainy afternoon was preceded by a sunny morning. There were 11 sunny mornings and 12 sunny afternoons. How long was the vacation?

Answer: 18 days of vacation.

Solution: 13 of the days of vacation were half sunny and half rainy. As there were 23 sunny mornings and afternoons (11 sunny mornings+12 sunny afternoons = 23 sunny mornings and afternoons), 13 of those sunny afternoons or mornings were on half rainy days. This means there are 10 sunny half-days left over, which equal 5 sunny full days. The 5 sunny full days plus the 13 half sunny/rainy days equal 18 total days of vacation.

23. Suppose you overhear the following conversation: Paul: How old are your three children? Paula: The product of their ages is 36 and the sum of their ages is the same as today's date. Paul: That is not enough information. Paula: The oldest child also has red hair. If you were Paul could you determine the ages of Paula's children? Explain.

Answer: If I were Paul this might be possible, but since we don’t know the date that Paula said this, it is not possible for us to find out.

Solution: There are many different combinations of three numbers that can be multiplied and will produce 36. As we do not know the date that Paula said this, the only thing we can be sure of is that the sum of the ages is less than 31 because no month has more than 31 days. Unfortunately, only one set of ages (ages 1 year old, 1 year old and 36 years old) has a sum greater than 31, which leaves many possible combinations open as possible. For today’s date, the 13th, ages of 2, 2, and 9 would produce 36 and have a sum of 13, but, again, it is uncertain. If it were the first of the month, there would be no possible combinations that would produce 36 and sum 1.

24. Two candles of equal length were lit at the same time. One candle took 6 hr to burn out and the other candle took 3 hr to burn out. After how much time was one candle exactly twice as long as the other candle?

Answer: 2 hours.

Solution: The faster burning candle took half the time to burn as the slower burning candle (3 hours/ 6 hours = 1/2), meaning it burned twice as fast. This means that after 2/3 of the total burning time for the faster burning candle it will be 1/3 of its original height and at the slower burning candle will be at 2/3 of its original height and 1/3 is half of 2/3. Since the faster burning candle took 3 hours to burn, 2/3 of its total burning time is 2 hours.

25. Two candles of length L and L + 1 were lit at 6:00 and 4:30, respectively. At 8:30 they had the same length. The longer candle died at 10:30 and the shorter candle died at 10:00. Find L.

Answer: L=2.

Solution: The shorter candle lasted for 4 hours and the longer candle lasted for 6 hours. As 6 hours – 4 hours = 2 hours and 2 hours / 4 hours = 1/2, the longer candle lasted 50% longer and was, therefore, 50% longer in length. This means that the +1 in L+1 on the longer candle was 1/2 of L. 1/2L=1, so L=2*1, L=2.

Course:MATH110/Archive/2010-2011/003/Groups/Group 18

2010-11-12T05:22:23Z

RolandWill: /* 2.A lady did not have her driver's license with her when she failed to stop at a stop sign and then went three blocks down a one-way street the wrong way. A policeman saw her, but he did not stop her. Explain. */

{{Infobox MATH110 Groups
| group number = 18
| member 1 = [[User:ChouJuChen|Audrey Chen]]
| member 2 = [[User:SifatHasan|Sifat Hasan]]
| member 3 = [[User:CaitlinLastiwkaFarquharson|Caitlin Lastiwka-Farquharson]]
| member 4 = [[User:VictoriaWall|Victoria Wall]]
| member 5 = [[User:RolandWill|Roland Will]]
| member 6 =
}}

==Sub-Pages==

Basic Skills Project [http://wiki.ubc.ca/Course:MATH110/003/Groups/Group_18/Basic_Skills_Project]

==Homework due October 20th, 2010==

I created a page for our homework due tomorrow: [http://wiki.ubc.ca/Course:MATH110/003/Groups/Group_18/Homework_October_20th,_2010 http://wiki.ubc.ca/Course:MATH110/003/Groups/Group 18/Homework October 20th, 2010]

-Roland

I've moved the page, it was missing the ''Course:'' part which means it was created directly inside the wiki and not as a subpage of your group page, which is something the wiki admins don't like that much. By the way, you're allowed to use spaces in the name of your pages.

-- [[User:DavidKohler|DavidKohler]] 06:28, 20 October 2010 (UTC)

1-5

Victoria Wall

1.A bus traveled from the terminal to the airport at an average speed of 30 mi/hr and the trip took an hour and 20 min. The bus then traveled from the airport back to the terminal and again averaged 30 mi/hr. However, the return trip required 80 min. Explain.

' 'Lets call the terminal T and the airport A. If the bus travelled from T to A at 30mi/hr and it took them one hour and 20 mins to get from T to A at this speed, and there are 60 minutes in one hour, it took the bus 60min + 20min to get to A which is a total of 80min. The bus took 80 min to get from T to A. To get from A to T at the same speed (30mi/hr) it took the bus 80min. 80min = 80 min. This means going from A to T or vis versa at 30 mi/hr it will take the bus 80min.

2.A lady did not have her driver's license with her when she failed to stop at a stop sign and then went three blocks down a one-way street the wrong way. A policeman saw her, but he did not stop her. Explain.

' 'The lady was walking. It never says she was driving.

==3.One of three boxes contains apples, another box contains oranges, and another box contains a mixture of apples and oranges. The boxes are labeled APPLES, ORANGES and APPLES AND ORANGES, but each label is incorrect. Can you select one fruit from only one box and determine the correct labels? Explain. ==

' 'if you selecet from the box APPLES AND ORANGES then you will be able to see the labels if they are correct or not.

==4.I am the brother of the blind fiddler, but brothers I have none. How can this be? ==

' 'Since it says that he is the brother of the blind fiddler it does not mean that the fiddle is male, since he has no brothers than the fiddler must be a female.

==5.Two quarters rest next to each other on a table. One coin is held fixed while the second coin is rolled around the edge of the first coin with no slipping. When the moving coin returns to its original position, how many times has it revolved? ==

' 'This is because the moving quarters revolves two full revolutions

==6-10==
== Caitlin Lastiwka- Farquharson ==

==6. Three kinds of apples are all mixed up in a basket. How many apples must you draw without (without looking) from the basket to be sure of getting at least two of a kind? ==

' ' To be sure you are getting at least two of a kind, you must select all of the other types of apples, plus two more. Meaning that only once you have selected all of the other apples can you be sure that you will select two of the kind you desire. It can be written like this: x,a x2, b and x3, c, with x representing the quantity of apples. This can be calculated by x2 + x3 +2. X2 representing one of the types of apples, x3 representing the other type and 2 representing 2 of the kind of apples you are trying to select. This is the only way to be sure you are getting at least two of a kind. ' '

==7. Suppose you have 40 blue socks and 40 brown socks in a drawer. How many socks must you take from the drawer (without looking) to be sure of getting (i) a pair of the same colour, and (ii) a pair with different colors. ==

' 'You must take three socks from the drawer to ensure you have a pair that match. This is because if you only select two, one could be brown and one could be blue. Selecting three, ensures that at least two of them will be the same colour. As for part two, you would need to select 41 socks to ensure you had a pair of different coloured socks because if you select 40 or less you could get all the same colour, but selecting 41 ensures you will have at least one pair of mixed colour. ' '

==8. Rueben says "Two days ago I was 20 years old. Later next year I will be 23 years old." Explain how this is possible. ==

' 'It is possible if your birthday is on the 31st of December and today is the 1st of January. This is because on the 30th of December (two days ago) you we’re 20 years old and now you are 21, later this year you will turn 22 on the 31st of December, and therefore 23 the next year.' '

==9. A rope ladder hanging over the side of a boat has rungs one foot apart. Ten rungs are showing. If the tide rises five feet, how many rungs will be showing? ==

' ' 5 rungs will be showing, because if there are 10 showing now, and they are each a foot apart, then for 5 more rungs to be showing there would need to be an increase in the level of water by 5 feet. ' '

==10.Suppose one-half of all people are chocolate eaters and one-half of all people are women. (i) Does it follow that one-fourth of all people are women chocolate eaters? (ii) Does it follow that one-half of all men are chocolate eaters? Explain. ==

' ' No, it does not follow that one-fourth of all people are women chocolate eaters and it does not follow that half of all men are chocolate eaters because are completely independent scenarios. Meaning that the the amount of women there are does not influence the amount of men that will eat chocolate. For example, If 50% of people are women and 50% of the entire population including men and women eat chocolate (arrived at by using the same logic that if 1/4 of women eat chocolate and 1/4 of men eat chocolate), that entire 50% could be comprised of women, meaning that no men eat chocolate disproving the statement.

==11-14==
==Sifat Hasan==

==11 11. A woman, her older brother, her son, and her daughter are chess players. The worst player’s twin, who is one of the four players, and the best player are of opposite sex. The worst player and the best player have the same age. If this is possible, who is the worst player?==

The four players (according to age, from oldest to youngest) are: woman's older brother, woman, and the son and the daughter (of the same age). Assuming that the children are of the same age (i.e. twins), the worst player is one of them, since they are the only ones who can have a twin. Assuming that the worst player is the daughter, her brother the son, is of the opposite sex as the woman, therefore the woman is the worst player. However, since the worst and the best player are of the same age, this is not possible, because the twins are of the opposite sex and they are of different genders.

==12 A Manhattan fellow had a girlfriend in the Bronx and a girlfriend in Brooklyn. He decided which girlfriend to visit by arriving randomly at the train station and taking the first of the Bronx or Brooklyn trains that arrived. The trains to Brooklyn and the Bronx each arrived regularly every 10 minutes. Not long after he began his scheme the man's Bronx girlfriend left him because he rarely visited. Give a (logical) explanation==

Assuming that the Bronx and the Brooklyn train arrive one after the other every 10 minutes, the only logical explanation would be that the man in Manhattan coincidentally went to the station 10 minutes or less before a train to Brooklyn arrived, most of the time.

==13 If a clock takes 5 seconds to strike 5:00 (with 5 equally spaced chimes), how long does it take to strike 10:00 (with 10 equally spaced chimes)?==

If it takes 5 seconds to strike 5, there will be 4 little halts in the middle. Therefore it takes 5 chimes 4 (5/4) = 1.25 second halts to finish. For 10 chimes, there are 9 halts so, it takes 9x 1.25 = 11.25 seconds for 10 halts.

==14 One day in the maternity ward, the name tags for four girl babies became mixed up. (i) In how many different ways could two of the babies be tagged correctly and two of the babies be tagged incorrectly? (ii) In how many different ways could three of the babies be tagged correctly and one baby be tagged incorrectly?==

(i)and (ii) If we take the babies names as A,B,C and D. There are 6 different combinations of the mix up, that two babies' names can be correct and 2 can be wrong. Assuming the name tags for the babies A,B,C and D are in respective order, they are ABDC, ADCB, ACBD, DBCA, CBAD and BACD. All other combinations for example BCAD will have one correct and 3 incorrect, or all four of them correct, because if 3 are correct, the fourth one has to be correct.

==15-16==
==Roland Will==

==15. Alex says to you, “I'll bet you any amount of money that if I shuffle this deck of cards, there will always be as many red cards in the first half of the deck as there are black cards in the second half of the deck.” Should you accept his bet?==

Answer: No, you shouldn't assuming the deck has equal amounts of red and black cards as in a standard 52 card deck.
Solution: In a standard 52 card deck, half of the cards (26) are black and half are red. If you take 26 cards at random from the deck, x of them will be black and y of them will be red, and x+y=26. As there are 26 of each color in the deck, then x+?=26 for the black cards in the deck and ?+y=26 for the red cards in the deck. As x+y=26 in the first randomly selected 26 cards, then the value of black cards in the other half of the deck must equal y, and the value of red cards in the other half of the deck must equal x meaning that "there will always be as many red cards in the first half of the deck as there are black cards in the second half of the deck."

==16. Suppose that each daughter in your family has the same number of brothers as she has sisters, and each son in your family has twice as many sisters as he has brothers. How many sons and daughters are in the family?==

Answer:3 total, 2 sister and 1 brother
Solution: Since the daughters in the family each have as many brothers as sisters the amount of sisters, with x standing for the amount of brothers, is x+1. As each brother has twice as many sisters as brothers, the amount of sisters must equal 2(x-1) or 2x-2. To find the number of brother: x+1=2x+1, 1=x-2, 3=x, which means that their are 3 brothers and 4 sisters (x+1= the number of sisters and x=3). This makes sense because a sister would have an equal amount of brothers to sisters, 3 sisters and 3 brothers, if there were 4 sisters and 3 brothers total, and each brother would have 4 sisters and 3 brothers, which is twice the amount of brothers to sisters.

==17~21==
==Audrey Chen==

==17.The zero point on a bathroom scale is set incorrectly, but otherwise the scale is accurate. It shows 60 kg when Dan stands on the scale, 50 kg when Sarah stands on the scale, but 105 kg when Dan and Sarah both stand on the scale. Does the scale read too high or too low? Explain. ==

''The scale read too low, since Dan is shown as 60kg and Sarah is 50kg, suppose 60+50=110, 105-110=-5, so that means the scale is smaller than 0 in the beginning''

==18. Alice takes one-third of the pennies from a large jar. Then Bret takes one-third of the remaining pennies from the jar. Finally, Carla takes one-third of the remaining pennies from the jar, leaving 40 pennies in the jar. How many pennies were in the jar at the start? ==

''If the total pennies is "x", Alice take 1/3x, so it has 2/3x left after Alice took it, than Bret take 1/3 out, after Alice took it, which is 2/3x*1/3= 2/9x, so in the beginning they have x, after Alice took it, it has 2/3x left, and Bret took 2/9x, so after Bret took it, it becomes 2/3x-2/9x= 4/9x-2/9x=2/9x left in the jar. Than Carla take 1/3 of the rest, so she took 1/3 of rest which is 2/9x*1/3=3/27x, so Alice took 1/3x, Bret tool 2/9x, Carla took 3/27x, three of them totaly took 1/3x+2/9x+3/27x=18/27x, so there still has x-18/27x= 9/27x= 1/3 left, 1/3x=40pennies, so x=120 pennies, so it was having 120 pennies in the jar.

==19. One morning each member of Angela's family drank an eight-ounce cup of coffee and milk, with the (nonzero) amounts of coffee and milk varying from cup to cup. Angela drank a quarter of the total amount of milk and a sixth of the total amount of coffee. What is the least number of people in the family? ==

''If we let total milk is x, total coffee is y. Than 1/4x+1/6y=8, and because every cup is 8ounce, x+y is multiple by 8. So make it easier, we use 1/4x+1/6y=8 * 12 to both sides. than we will got 3x+2y=96, now we have 3x+2y=96 and x+y is multiple of 8, and the number that multiple by 8 is 8, 16, 24, 32... so 2x+2y= 16, 32, 48, 64, 80, 96, since 3x+2y=96, it can't be more than 96. It will only have 6 possible number, so if you take 3x+2y=96 substracting 2x+2y=16, 32, 48, 64, 80, 96 you can get 6 possible x, which are 80, 64, 48, 32, 16, and 0. Than put the number into 3x+2y=96, if you put 80 in, will get 20, which is bigger than 8, and also 64, 48. If we use 32, it will equal to 8, but that means we have 0 coffee, but coffee can't be 0, so there's only 16 and 0 left. Since Angela had 1/4 of total amount of milk, milk can't be 0. So we got 16ounce than 16*(1/4)=4, so that means she had 8-4=4 's coffee. So 4=1/6 coffee, than the total amount of coffee would be 4*6=24. than x=16 and y=24, 16+24=40 40/8ounce=5, so at least have 5 cups of drinks, so that means at least they have 5 members in Angela's family.''

==20.Of two clocks next to each other, one runs 5 min per hour fast and the other runs 5 min per hour slow. At midnight the clocks show the same time. At what time are they are one hour apart? ==

''Since one clock runs 5 min faster per hour, the other is 5 min slower, after clock runs an hour, two clocks will have 10 min different from each other. 60 min an hour. 60/10=6, so after 6 hours two clocks will having one hour apart, and that would be 6AM.''

==21.Sven placed exactly in the middle among all runners in a race. Dan was slower than Sven, in 10th place, and Lars was in 16th place. How many runners were in the race? ==

''There were 17 runners. Since lars was in 16th place, the runners at least have to be 16, than if Sven is placed exactly in the middle, it means it would have even number of runners. Because Dan is slower and he was at 10 place that tells us Seven has to be before 10th, and if there has 19 runners, Sven and Dan would be at the same place, so it should be 17 runners, than Sven would be at exactly in the middle which at 9th place.''

==22-25==

Roland Will

22. During a vacation, it rained on 13 days, but when it rained in the morning, the afternoon was sunny, and every rainy afternoon was preceded by a sunny morning. There were 11 sunny mornings and 12 sunny afternoons. How long was the vacation?

Answer: 18 days of vacation.

Solution: 13 of the days of vacation were half sunny and half rainy. As there were 23 sunny mornings and afternoons (11 sunny mornings+12 sunny afternoons = 23 sunny mornings and afternoons), 13 of those sunny afternoons or mornings were on half rainy days. This means there are 10 sunny half-days left over, which equal 5 sunny full days. The 5 sunny full days plus the 13 half sunny/rainy days equal 18 total days of vacation.

23. Suppose you overhear the following conversation: Paul: How old are your three children? Paula: The product of their ages is 36 and the sum of their ages is the same as today's date. Paul: That is not enough information. Paula: The oldest child also has red hair. If you were Paul could you determine the ages of Paula's children? Explain.

Answer: If I were Paul this might be possible, but since we don’t know the date that Paula said this, it is not possible for us to find out.

Solution: There are many different combinations of three numbers that can be multiplied and will produce 36. As we do not know the date that Paula said this, the only thing we can be sure of is that the sum of the ages is less than 31 because no month has more than 31 days. Unfortunately, only one set of ages (ages 1 year old, 1 year old and 36 years old) has a sum greater than 31, which leaves many possible combinations open as possible. For today’s date, the 13th, ages of 2, 2, and 9 would produce 36 and have a sum of 13, but, again, it is uncertain. If it were the first of the month, there would be no possible combinations that would produce 36 and sum 1.

24. Two candles of equal length were lit at the same time. One candle took 6 hr to burn out and the other candle took 3 hr to burn out. After how much time was one candle exactly twice as long as the other candle?

Answer: 2 hours.

Solution: The faster burning candle took half the time to burn as the slower burning candle (3 hours/ 6 hours = 1/2), meaning it burned twice as fast. This means that after 2/3 of the total burning time for the faster burning candle it will be 1/3 of its original height and at the slower burning candle will be at 2/3 of its original height and 1/3 is half of 2/3. Since the faster burning candle took 3 hours to burn, 2/3 of its total burning time is 2 hours.

25. Two candles of length L and L + 1 were lit at 6:00 and 4:30, respectively. At 8:30 they had the same length. The longer candle died at 10:30 and the shorter candle died at 10:00. Find L.

Answer: L=2.

Solution: The shorter candle lasted for 4 hours and the longer candle lasted for 6 hours. As 6 hours – 4 hours = 2 hours and 2 hours / 4 hours = 1/2, the longer candle lasted 50% longer and was, therefore, 50% longer in length. This means that the +1 in L+1 on the longer candle was 1/2 of L. 1/2L=1, so L=2*1, L=2.

Course:MATH110/Archive/2010-2011/003/Groups/Group 18

2010-11-12T05:22:13Z

RolandWill: /* 1.A bus traveled from the terminal to the airport at an average speed of 30 mi/hr and the trip took an hour and 20 min. The bus then traveled from the airport back to the terminal and again averaged 30 mi/hr. However, the return trip required 80 m

{{Infobox MATH110 Groups
| group number = 18
| member 1 = [[User:ChouJuChen|Audrey Chen]]
| member 2 = [[User:SifatHasan|Sifat Hasan]]
| member 3 = [[User:CaitlinLastiwkaFarquharson|Caitlin Lastiwka-Farquharson]]
| member 4 = [[User:VictoriaWall|Victoria Wall]]
| member 5 = [[User:RolandWill|Roland Will]]
| member 6 =
}}

==Sub-Pages==

Basic Skills Project [http://wiki.ubc.ca/Course:MATH110/003/Groups/Group_18/Basic_Skills_Project]

==Homework due October 20th, 2010==

I created a page for our homework due tomorrow: [http://wiki.ubc.ca/Course:MATH110/003/Groups/Group_18/Homework_October_20th,_2010 http://wiki.ubc.ca/Course:MATH110/003/Groups/Group 18/Homework October 20th, 2010]

-Roland

I've moved the page, it was missing the ''Course:'' part which means it was created directly inside the wiki and not as a subpage of your group page, which is something the wiki admins don't like that much. By the way, you're allowed to use spaces in the name of your pages.

-- [[User:DavidKohler|DavidKohler]] 06:28, 20 October 2010 (UTC)

1-5

Victoria Wall

1.A bus traveled from the terminal to the airport at an average speed of 30 mi/hr and the trip took an hour and 20 min. The bus then traveled from the airport back to the terminal and again averaged 30 mi/hr. However, the return trip required 80 min. Explain.

' 'Lets call the terminal T and the airport A. If the bus travelled from T to A at 30mi/hr and it took them one hour and 20 mins to get from T to A at this speed, and there are 60 minutes in one hour, it took the bus 60min + 20min to get to A which is a total of 80min. The bus took 80 min to get from T to A. To get from A to T at the same speed (30mi/hr) it took the bus 80min. 80min = 80 min. This means going from A to T or vis versa at 30 mi/hr it will take the bus 80min.

==2.A lady did not have her driver's license with her when she failed to stop at a stop sign and then went three blocks down a one-way street the wrong way. A policeman saw her, but he did not stop her. Explain. ==

' 'The lady was walking. It never says she was driving.

==3.One of three boxes contains apples, another box contains oranges, and another box contains a mixture of apples and oranges. The boxes are labeled APPLES, ORANGES and APPLES AND ORANGES, but each label is incorrect. Can you select one fruit from only one box and determine the correct labels? Explain. ==

' 'if you selecet from the box APPLES AND ORANGES then you will be able to see the labels if they are correct or not.

==4.I am the brother of the blind fiddler, but brothers I have none. How can this be? ==

' 'Since it says that he is the brother of the blind fiddler it does not mean that the fiddle is male, since he has no brothers than the fiddler must be a female.

==5.Two quarters rest next to each other on a table. One coin is held fixed while the second coin is rolled around the edge of the first coin with no slipping. When the moving coin returns to its original position, how many times has it revolved? ==

' 'This is because the moving quarters revolves two full revolutions

==6-10==
== Caitlin Lastiwka- Farquharson ==

==6. Three kinds of apples are all mixed up in a basket. How many apples must you draw without (without looking) from the basket to be sure of getting at least two of a kind? ==

' ' To be sure you are getting at least two of a kind, you must select all of the other types of apples, plus two more. Meaning that only once you have selected all of the other apples can you be sure that you will select two of the kind you desire. It can be written like this: x,a x2, b and x3, c, with x representing the quantity of apples. This can be calculated by x2 + x3 +2. X2 representing one of the types of apples, x3 representing the other type and 2 representing 2 of the kind of apples you are trying to select. This is the only way to be sure you are getting at least two of a kind. ' '

==7. Suppose you have 40 blue socks and 40 brown socks in a drawer. How many socks must you take from the drawer (without looking) to be sure of getting (i) a pair of the same colour, and (ii) a pair with different colors. ==

' 'You must take three socks from the drawer to ensure you have a pair that match. This is because if you only select two, one could be brown and one could be blue. Selecting three, ensures that at least two of them will be the same colour. As for part two, you would need to select 41 socks to ensure you had a pair of different coloured socks because if you select 40 or less you could get all the same colour, but selecting 41 ensures you will have at least one pair of mixed colour. ' '

==8. Rueben says "Two days ago I was 20 years old. Later next year I will be 23 years old." Explain how this is possible. ==

' 'It is possible if your birthday is on the 31st of December and today is the 1st of January. This is because on the 30th of December (two days ago) you we’re 20 years old and now you are 21, later this year you will turn 22 on the 31st of December, and therefore 23 the next year.' '

==9. A rope ladder hanging over the side of a boat has rungs one foot apart. Ten rungs are showing. If the tide rises five feet, how many rungs will be showing? ==

' ' 5 rungs will be showing, because if there are 10 showing now, and they are each a foot apart, then for 5 more rungs to be showing there would need to be an increase in the level of water by 5 feet. ' '

==10.Suppose one-half of all people are chocolate eaters and one-half of all people are women. (i) Does it follow that one-fourth of all people are women chocolate eaters? (ii) Does it follow that one-half of all men are chocolate eaters? Explain. ==

' ' No, it does not follow that one-fourth of all people are women chocolate eaters and it does not follow that half of all men are chocolate eaters because are completely independent scenarios. Meaning that the the amount of women there are does not influence the amount of men that will eat chocolate. For example, If 50% of people are women and 50% of the entire population including men and women eat chocolate (arrived at by using the same logic that if 1/4 of women eat chocolate and 1/4 of men eat chocolate), that entire 50% could be comprised of women, meaning that no men eat chocolate disproving the statement.

==11-14==
==Sifat Hasan==

==11 11. A woman, her older brother, her son, and her daughter are chess players. The worst player’s twin, who is one of the four players, and the best player are of opposite sex. The worst player and the best player have the same age. If this is possible, who is the worst player?==

The four players (according to age, from oldest to youngest) are: woman's older brother, woman, and the son and the daughter (of the same age). Assuming that the children are of the same age (i.e. twins), the worst player is one of them, since they are the only ones who can have a twin. Assuming that the worst player is the daughter, her brother the son, is of the opposite sex as the woman, therefore the woman is the worst player. However, since the worst and the best player are of the same age, this is not possible, because the twins are of the opposite sex and they are of different genders.

==12 A Manhattan fellow had a girlfriend in the Bronx and a girlfriend in Brooklyn. He decided which girlfriend to visit by arriving randomly at the train station and taking the first of the Bronx or Brooklyn trains that arrived. The trains to Brooklyn and the Bronx each arrived regularly every 10 minutes. Not long after he began his scheme the man's Bronx girlfriend left him because he rarely visited. Give a (logical) explanation==

Assuming that the Bronx and the Brooklyn train arrive one after the other every 10 minutes, the only logical explanation would be that the man in Manhattan coincidentally went to the station 10 minutes or less before a train to Brooklyn arrived, most of the time.

==13 If a clock takes 5 seconds to strike 5:00 (with 5 equally spaced chimes), how long does it take to strike 10:00 (with 10 equally spaced chimes)?==

If it takes 5 seconds to strike 5, there will be 4 little halts in the middle. Therefore it takes 5 chimes 4 (5/4) = 1.25 second halts to finish. For 10 chimes, there are 9 halts so, it takes 9x 1.25 = 11.25 seconds for 10 halts.

==14 One day in the maternity ward, the name tags for four girl babies became mixed up. (i) In how many different ways could two of the babies be tagged correctly and two of the babies be tagged incorrectly? (ii) In how many different ways could three of the babies be tagged correctly and one baby be tagged incorrectly?==

(i)and (ii) If we take the babies names as A,B,C and D. There are 6 different combinations of the mix up, that two babies' names can be correct and 2 can be wrong. Assuming the name tags for the babies A,B,C and D are in respective order, they are ABDC, ADCB, ACBD, DBCA, CBAD and BACD. All other combinations for example BCAD will have one correct and 3 incorrect, or all four of them correct, because if 3 are correct, the fourth one has to be correct.

==15-16==
==Roland Will==

==15. Alex says to you, “I'll bet you any amount of money that if I shuffle this deck of cards, there will always be as many red cards in the first half of the deck as there are black cards in the second half of the deck.” Should you accept his bet?==

Answer: No, you shouldn't assuming the deck has equal amounts of red and black cards as in a standard 52 card deck.
Solution: In a standard 52 card deck, half of the cards (26) are black and half are red. If you take 26 cards at random from the deck, x of them will be black and y of them will be red, and x+y=26. As there are 26 of each color in the deck, then x+?=26 for the black cards in the deck and ?+y=26 for the red cards in the deck. As x+y=26 in the first randomly selected 26 cards, then the value of black cards in the other half of the deck must equal y, and the value of red cards in the other half of the deck must equal x meaning that "there will always be as many red cards in the first half of the deck as there are black cards in the second half of the deck."

==16. Suppose that each daughter in your family has the same number of brothers as she has sisters, and each son in your family has twice as many sisters as he has brothers. How many sons and daughters are in the family?==

Answer:3 total, 2 sister and 1 brother
Solution: Since the daughters in the family each have as many brothers as sisters the amount of sisters, with x standing for the amount of brothers, is x+1. As each brother has twice as many sisters as brothers, the amount of sisters must equal 2(x-1) or 2x-2. To find the number of brother: x+1=2x+1, 1=x-2, 3=x, which means that their are 3 brothers and 4 sisters (x+1= the number of sisters and x=3). This makes sense because a sister would have an equal amount of brothers to sisters, 3 sisters and 3 brothers, if there were 4 sisters and 3 brothers total, and each brother would have 4 sisters and 3 brothers, which is twice the amount of brothers to sisters.

==17~21==
==Audrey Chen==

==17.The zero point on a bathroom scale is set incorrectly, but otherwise the scale is accurate. It shows 60 kg when Dan stands on the scale, 50 kg when Sarah stands on the scale, but 105 kg when Dan and Sarah both stand on the scale. Does the scale read too high or too low? Explain. ==

''The scale read too low, since Dan is shown as 60kg and Sarah is 50kg, suppose 60+50=110, 105-110=-5, so that means the scale is smaller than 0 in the beginning''

==18. Alice takes one-third of the pennies from a large jar. Then Bret takes one-third of the remaining pennies from the jar. Finally, Carla takes one-third of the remaining pennies from the jar, leaving 40 pennies in the jar. How many pennies were in the jar at the start? ==

''If the total pennies is "x", Alice take 1/3x, so it has 2/3x left after Alice took it, than Bret take 1/3 out, after Alice took it, which is 2/3x*1/3= 2/9x, so in the beginning they have x, after Alice took it, it has 2/3x left, and Bret took 2/9x, so after Bret took it, it becomes 2/3x-2/9x= 4/9x-2/9x=2/9x left in the jar. Than Carla take 1/3 of the rest, so she took 1/3 of rest which is 2/9x*1/3=3/27x, so Alice took 1/3x, Bret tool 2/9x, Carla took 3/27x, three of them totaly took 1/3x+2/9x+3/27x=18/27x, so there still has x-18/27x= 9/27x= 1/3 left, 1/3x=40pennies, so x=120 pennies, so it was having 120 pennies in the jar.

==19. One morning each member of Angela's family drank an eight-ounce cup of coffee and milk, with the (nonzero) amounts of coffee and milk varying from cup to cup. Angela drank a quarter of the total amount of milk and a sixth of the total amount of coffee. What is the least number of people in the family? ==

''If we let total milk is x, total coffee is y. Than 1/4x+1/6y=8, and because every cup is 8ounce, x+y is multiple by 8. So make it easier, we use 1/4x+1/6y=8 * 12 to both sides. than we will got 3x+2y=96, now we have 3x+2y=96 and x+y is multiple of 8, and the number that multiple by 8 is 8, 16, 24, 32... so 2x+2y= 16, 32, 48, 64, 80, 96, since 3x+2y=96, it can't be more than 96. It will only have 6 possible number, so if you take 3x+2y=96 substracting 2x+2y=16, 32, 48, 64, 80, 96 you can get 6 possible x, which are 80, 64, 48, 32, 16, and 0. Than put the number into 3x+2y=96, if you put 80 in, will get 20, which is bigger than 8, and also 64, 48. If we use 32, it will equal to 8, but that means we have 0 coffee, but coffee can't be 0, so there's only 16 and 0 left. Since Angela had 1/4 of total amount of milk, milk can't be 0. So we got 16ounce than 16*(1/4)=4, so that means she had 8-4=4 's coffee. So 4=1/6 coffee, than the total amount of coffee would be 4*6=24. than x=16 and y=24, 16+24=40 40/8ounce=5, so at least have 5 cups of drinks, so that means at least they have 5 members in Angela's family.''

==20.Of two clocks next to each other, one runs 5 min per hour fast and the other runs 5 min per hour slow. At midnight the clocks show the same time. At what time are they are one hour apart? ==

''Since one clock runs 5 min faster per hour, the other is 5 min slower, after clock runs an hour, two clocks will have 10 min different from each other. 60 min an hour. 60/10=6, so after 6 hours two clocks will having one hour apart, and that would be 6AM.''

==21.Sven placed exactly in the middle among all runners in a race. Dan was slower than Sven, in 10th place, and Lars was in 16th place. How many runners were in the race? ==

''There were 17 runners. Since lars was in 16th place, the runners at least have to be 16, than if Sven is placed exactly in the middle, it means it would have even number of runners. Because Dan is slower and he was at 10 place that tells us Seven has to be before 10th, and if there has 19 runners, Sven and Dan would be at the same place, so it should be 17 runners, than Sven would be at exactly in the middle which at 9th place.''

==22-25==

Roland Will

22. During a vacation, it rained on 13 days, but when it rained in the morning, the afternoon was sunny, and every rainy afternoon was preceded by a sunny morning. There were 11 sunny mornings and 12 sunny afternoons. How long was the vacation?

Answer: 18 days of vacation.

Solution: 13 of the days of vacation were half sunny and half rainy. As there were 23 sunny mornings and afternoons (11 sunny mornings+12 sunny afternoons = 23 sunny mornings and afternoons), 13 of those sunny afternoons or mornings were on half rainy days. This means there are 10 sunny half-days left over, which equal 5 sunny full days. The 5 sunny full days plus the 13 half sunny/rainy days equal 18 total days of vacation.

23. Suppose you overhear the following conversation: Paul: How old are your three children? Paula: The product of their ages is 36 and the sum of their ages is the same as today's date. Paul: That is not enough information. Paula: The oldest child also has red hair. If you were Paul could you determine the ages of Paula's children? Explain.

Answer: If I were Paul this might be possible, but since we don’t know the date that Paula said this, it is not possible for us to find out.

Solution: There are many different combinations of three numbers that can be multiplied and will produce 36. As we do not know the date that Paula said this, the only thing we can be sure of is that the sum of the ages is less than 31 because no month has more than 31 days. Unfortunately, only one set of ages (ages 1 year old, 1 year old and 36 years old) has a sum greater than 31, which leaves many possible combinations open as possible. For today’s date, the 13th, ages of 2, 2, and 9 would produce 36 and have a sum of 13, but, again, it is uncertain. If it were the first of the month, there would be no possible combinations that would produce 36 and sum 1.

24. Two candles of equal length were lit at the same time. One candle took 6 hr to burn out and the other candle took 3 hr to burn out. After how much time was one candle exactly twice as long as the other candle?

Answer: 2 hours.

Solution: The faster burning candle took half the time to burn as the slower burning candle (3 hours/ 6 hours = 1/2), meaning it burned twice as fast. This means that after 2/3 of the total burning time for the faster burning candle it will be 1/3 of its original height and at the slower burning candle will be at 2/3 of its original height and 1/3 is half of 2/3. Since the faster burning candle took 3 hours to burn, 2/3 of its total burning time is 2 hours.

25. Two candles of length L and L + 1 were lit at 6:00 and 4:30, respectively. At 8:30 they had the same length. The longer candle died at 10:30 and the shorter candle died at 10:00. Find L.

Answer: L=2.

Solution: The shorter candle lasted for 4 hours and the longer candle lasted for 6 hours. As 6 hours – 4 hours = 2 hours and 2 hours / 4 hours = 1/2, the longer candle lasted 50% longer and was, therefore, 50% longer in length. This means that the +1 in L+1 on the longer candle was 1/2 of L. 1/2L=1, so L=2*1, L=2.

Course:MATH110/Archive/2010-2011/003/Groups/Group 18

2010-11-12T05:22:02Z

RolandWill: /* Victoria Wall */

{{Infobox MATH110 Groups
| group number = 18
| member 1 = [[User:ChouJuChen|Audrey Chen]]
| member 2 = [[User:SifatHasan|Sifat Hasan]]
| member 3 = [[User:CaitlinLastiwkaFarquharson|Caitlin Lastiwka-Farquharson]]
| member 4 = [[User:VictoriaWall|Victoria Wall]]
| member 5 = [[User:RolandWill|Roland Will]]
| member 6 =
}}

==Sub-Pages==

Basic Skills Project [http://wiki.ubc.ca/Course:MATH110/003/Groups/Group_18/Basic_Skills_Project]

==Homework due October 20th, 2010==

I created a page for our homework due tomorrow: [http://wiki.ubc.ca/Course:MATH110/003/Groups/Group_18/Homework_October_20th,_2010 http://wiki.ubc.ca/Course:MATH110/003/Groups/Group 18/Homework October 20th, 2010]

-Roland

I've moved the page, it was missing the ''Course:'' part which means it was created directly inside the wiki and not as a subpage of your group page, which is something the wiki admins don't like that much. By the way, you're allowed to use spaces in the name of your pages.

-- [[User:DavidKohler|DavidKohler]] 06:28, 20 October 2010 (UTC)

1-5

Victoria Wall

==1.A bus traveled from the terminal to the airport at an average speed of 30 mi/hr and the trip took an hour and 20 min. The bus then traveled from the airport back to the terminal and again averaged 30 mi/hr. However, the return trip required 80 min. Explain.==

' 'Lets call the terminal T and the airport A. If the bus travelled from T to A at 30mi/hr and it took them one hour and 20 mins to get from T to A at this speed, and there are 60 minutes in one hour, it took the bus 60min + 20min to get to A which is a total of 80min. The bus took 80 min to get from T to A. To get from A to T at the same speed (30mi/hr) it took the bus 80min. 80min = 80 min. This means going from A to T or vis versa at 30 mi/hr it will take the bus 80min.

==2.A lady did not have her driver's license with her when she failed to stop at a stop sign and then went three blocks down a one-way street the wrong way. A policeman saw her, but he did not stop her. Explain. ==

' 'The lady was walking. It never says she was driving.

==3.One of three boxes contains apples, another box contains oranges, and another box contains a mixture of apples and oranges. The boxes are labeled APPLES, ORANGES and APPLES AND ORANGES, but each label is incorrect. Can you select one fruit from only one box and determine the correct labels? Explain. ==

' 'if you selecet from the box APPLES AND ORANGES then you will be able to see the labels if they are correct or not.

==4.I am the brother of the blind fiddler, but brothers I have none. How can this be? ==

' 'Since it says that he is the brother of the blind fiddler it does not mean that the fiddle is male, since he has no brothers than the fiddler must be a female.

==5.Two quarters rest next to each other on a table. One coin is held fixed while the second coin is rolled around the edge of the first coin with no slipping. When the moving coin returns to its original position, how many times has it revolved? ==

' 'This is because the moving quarters revolves two full revolutions

==6-10==
== Caitlin Lastiwka- Farquharson ==

==6. Three kinds of apples are all mixed up in a basket. How many apples must you draw without (without looking) from the basket to be sure of getting at least two of a kind? ==

' ' To be sure you are getting at least two of a kind, you must select all of the other types of apples, plus two more. Meaning that only once you have selected all of the other apples can you be sure that you will select two of the kind you desire. It can be written like this: x,a x2, b and x3, c, with x representing the quantity of apples. This can be calculated by x2 + x3 +2. X2 representing one of the types of apples, x3 representing the other type and 2 representing 2 of the kind of apples you are trying to select. This is the only way to be sure you are getting at least two of a kind. ' '

==7. Suppose you have 40 blue socks and 40 brown socks in a drawer. How many socks must you take from the drawer (without looking) to be sure of getting (i) a pair of the same colour, and (ii) a pair with different colors. ==

' 'You must take three socks from the drawer to ensure you have a pair that match. This is because if you only select two, one could be brown and one could be blue. Selecting three, ensures that at least two of them will be the same colour. As for part two, you would need to select 41 socks to ensure you had a pair of different coloured socks because if you select 40 or less you could get all the same colour, but selecting 41 ensures you will have at least one pair of mixed colour. ' '

==8. Rueben says "Two days ago I was 20 years old. Later next year I will be 23 years old." Explain how this is possible. ==

' 'It is possible if your birthday is on the 31st of December and today is the 1st of January. This is because on the 30th of December (two days ago) you we’re 20 years old and now you are 21, later this year you will turn 22 on the 31st of December, and therefore 23 the next year.' '

==9. A rope ladder hanging over the side of a boat has rungs one foot apart. Ten rungs are showing. If the tide rises five feet, how many rungs will be showing? ==

' ' 5 rungs will be showing, because if there are 10 showing now, and they are each a foot apart, then for 5 more rungs to be showing there would need to be an increase in the level of water by 5 feet. ' '

==10.Suppose one-half of all people are chocolate eaters and one-half of all people are women. (i) Does it follow that one-fourth of all people are women chocolate eaters? (ii) Does it follow that one-half of all men are chocolate eaters? Explain. ==

' ' No, it does not follow that one-fourth of all people are women chocolate eaters and it does not follow that half of all men are chocolate eaters because are completely independent scenarios. Meaning that the the amount of women there are does not influence the amount of men that will eat chocolate. For example, If 50% of people are women and 50% of the entire population including men and women eat chocolate (arrived at by using the same logic that if 1/4 of women eat chocolate and 1/4 of men eat chocolate), that entire 50% could be comprised of women, meaning that no men eat chocolate disproving the statement.

==11-14==
==Sifat Hasan==

==11 11. A woman, her older brother, her son, and her daughter are chess players. The worst player’s twin, who is one of the four players, and the best player are of opposite sex. The worst player and the best player have the same age. If this is possible, who is the worst player?==

The four players (according to age, from oldest to youngest) are: woman's older brother, woman, and the son and the daughter (of the same age). Assuming that the children are of the same age (i.e. twins), the worst player is one of them, since they are the only ones who can have a twin. Assuming that the worst player is the daughter, her brother the son, is of the opposite sex as the woman, therefore the woman is the worst player. However, since the worst and the best player are of the same age, this is not possible, because the twins are of the opposite sex and they are of different genders.

==12 A Manhattan fellow had a girlfriend in the Bronx and a girlfriend in Brooklyn. He decided which girlfriend to visit by arriving randomly at the train station and taking the first of the Bronx or Brooklyn trains that arrived. The trains to Brooklyn and the Bronx each arrived regularly every 10 minutes. Not long after he began his scheme the man's Bronx girlfriend left him because he rarely visited. Give a (logical) explanation==

Assuming that the Bronx and the Brooklyn train arrive one after the other every 10 minutes, the only logical explanation would be that the man in Manhattan coincidentally went to the station 10 minutes or less before a train to Brooklyn arrived, most of the time.

==13 If a clock takes 5 seconds to strike 5:00 (with 5 equally spaced chimes), how long does it take to strike 10:00 (with 10 equally spaced chimes)?==

If it takes 5 seconds to strike 5, there will be 4 little halts in the middle. Therefore it takes 5 chimes 4 (5/4) = 1.25 second halts to finish. For 10 chimes, there are 9 halts so, it takes 9x 1.25 = 11.25 seconds for 10 halts.

==14 One day in the maternity ward, the name tags for four girl babies became mixed up. (i) In how many different ways could two of the babies be tagged correctly and two of the babies be tagged incorrectly? (ii) In how many different ways could three of the babies be tagged correctly and one baby be tagged incorrectly?==

(i)and (ii) If we take the babies names as A,B,C and D. There are 6 different combinations of the mix up, that two babies' names can be correct and 2 can be wrong. Assuming the name tags for the babies A,B,C and D are in respective order, they are ABDC, ADCB, ACBD, DBCA, CBAD and BACD. All other combinations for example BCAD will have one correct and 3 incorrect, or all four of them correct, because if 3 are correct, the fourth one has to be correct.

==15-16==
==Roland Will==

==15. Alex says to you, “I'll bet you any amount of money that if I shuffle this deck of cards, there will always be as many red cards in the first half of the deck as there are black cards in the second half of the deck.” Should you accept his bet?==

Answer: No, you shouldn't assuming the deck has equal amounts of red and black cards as in a standard 52 card deck.
Solution: In a standard 52 card deck, half of the cards (26) are black and half are red. If you take 26 cards at random from the deck, x of them will be black and y of them will be red, and x+y=26. As there are 26 of each color in the deck, then x+?=26 for the black cards in the deck and ?+y=26 for the red cards in the deck. As x+y=26 in the first randomly selected 26 cards, then the value of black cards in the other half of the deck must equal y, and the value of red cards in the other half of the deck must equal x meaning that "there will always be as many red cards in the first half of the deck as there are black cards in the second half of the deck."

==16. Suppose that each daughter in your family has the same number of brothers as she has sisters, and each son in your family has twice as many sisters as he has brothers. How many sons and daughters are in the family?==

Answer:3 total, 2 sister and 1 brother
Solution: Since the daughters in the family each have as many brothers as sisters the amount of sisters, with x standing for the amount of brothers, is x+1. As each brother has twice as many sisters as brothers, the amount of sisters must equal 2(x-1) or 2x-2. To find the number of brother: x+1=2x+1, 1=x-2, 3=x, which means that their are 3 brothers and 4 sisters (x+1= the number of sisters and x=3). This makes sense because a sister would have an equal amount of brothers to sisters, 3 sisters and 3 brothers, if there were 4 sisters and 3 brothers total, and each brother would have 4 sisters and 3 brothers, which is twice the amount of brothers to sisters.

==17~21==
==Audrey Chen==

==17.The zero point on a bathroom scale is set incorrectly, but otherwise the scale is accurate. It shows 60 kg when Dan stands on the scale, 50 kg when Sarah stands on the scale, but 105 kg when Dan and Sarah both stand on the scale. Does the scale read too high or too low? Explain. ==

''The scale read too low, since Dan is shown as 60kg and Sarah is 50kg, suppose 60+50=110, 105-110=-5, so that means the scale is smaller than 0 in the beginning''

==18. Alice takes one-third of the pennies from a large jar. Then Bret takes one-third of the remaining pennies from the jar. Finally, Carla takes one-third of the remaining pennies from the jar, leaving 40 pennies in the jar. How many pennies were in the jar at the start? ==

''If the total pennies is "x", Alice take 1/3x, so it has 2/3x left after Alice took it, than Bret take 1/3 out, after Alice took it, which is 2/3x*1/3= 2/9x, so in the beginning they have x, after Alice took it, it has 2/3x left, and Bret took 2/9x, so after Bret took it, it becomes 2/3x-2/9x= 4/9x-2/9x=2/9x left in the jar. Than Carla take 1/3 of the rest, so she took 1/3 of rest which is 2/9x*1/3=3/27x, so Alice took 1/3x, Bret tool 2/9x, Carla took 3/27x, three of them totaly took 1/3x+2/9x+3/27x=18/27x, so there still has x-18/27x= 9/27x= 1/3 left, 1/3x=40pennies, so x=120 pennies, so it was having 120 pennies in the jar.

==19. One morning each member of Angela's family drank an eight-ounce cup of coffee and milk, with the (nonzero) amounts of coffee and milk varying from cup to cup. Angela drank a quarter of the total amount of milk and a sixth of the total amount of coffee. What is the least number of people in the family? ==

''If we let total milk is x, total coffee is y. Than 1/4x+1/6y=8, and because every cup is 8ounce, x+y is multiple by 8. So make it easier, we use 1/4x+1/6y=8 * 12 to both sides. than we will got 3x+2y=96, now we have 3x+2y=96 and x+y is multiple of 8, and the number that multiple by 8 is 8, 16, 24, 32... so 2x+2y= 16, 32, 48, 64, 80, 96, since 3x+2y=96, it can't be more than 96. It will only have 6 possible number, so if you take 3x+2y=96 substracting 2x+2y=16, 32, 48, 64, 80, 96 you can get 6 possible x, which are 80, 64, 48, 32, 16, and 0. Than put the number into 3x+2y=96, if you put 80 in, will get 20, which is bigger than 8, and also 64, 48. If we use 32, it will equal to 8, but that means we have 0 coffee, but coffee can't be 0, so there's only 16 and 0 left. Since Angela had 1/4 of total amount of milk, milk can't be 0. So we got 16ounce than 16*(1/4)=4, so that means she had 8-4=4 's coffee. So 4=1/6 coffee, than the total amount of coffee would be 4*6=24. than x=16 and y=24, 16+24=40 40/8ounce=5, so at least have 5 cups of drinks, so that means at least they have 5 members in Angela's family.''

==20.Of two clocks next to each other, one runs 5 min per hour fast and the other runs 5 min per hour slow. At midnight the clocks show the same time. At what time are they are one hour apart? ==

''Since one clock runs 5 min faster per hour, the other is 5 min slower, after clock runs an hour, two clocks will have 10 min different from each other. 60 min an hour. 60/10=6, so after 6 hours two clocks will having one hour apart, and that would be 6AM.''

==21.Sven placed exactly in the middle among all runners in a race. Dan was slower than Sven, in 10th place, and Lars was in 16th place. How many runners were in the race? ==

''There were 17 runners. Since lars was in 16th place, the runners at least have to be 16, than if Sven is placed exactly in the middle, it means it would have even number of runners. Because Dan is slower and he was at 10 place that tells us Seven has to be before 10th, and if there has 19 runners, Sven and Dan would be at the same place, so it should be 17 runners, than Sven would be at exactly in the middle which at 9th place.''

==22-25==

Roland Will

22. During a vacation, it rained on 13 days, but when it rained in the morning, the afternoon was sunny, and every rainy afternoon was preceded by a sunny morning. There were 11 sunny mornings and 12 sunny afternoons. How long was the vacation?

Answer: 18 days of vacation.

Solution: 13 of the days of vacation were half sunny and half rainy. As there were 23 sunny mornings and afternoons (11 sunny mornings+12 sunny afternoons = 23 sunny mornings and afternoons), 13 of those sunny afternoons or mornings were on half rainy days. This means there are 10 sunny half-days left over, which equal 5 sunny full days. The 5 sunny full days plus the 13 half sunny/rainy days equal 18 total days of vacation.

23. Suppose you overhear the following conversation: Paul: How old are your three children? Paula: The product of their ages is 36 and the sum of their ages is the same as today's date. Paul: That is not enough information. Paula: The oldest child also has red hair. If you were Paul could you determine the ages of Paula's children? Explain.

Answer: If I were Paul this might be possible, but since we don’t know the date that Paula said this, it is not possible for us to find out.

Solution: There are many different combinations of three numbers that can be multiplied and will produce 36. As we do not know the date that Paula said this, the only thing we can be sure of is that the sum of the ages is less than 31 because no month has more than 31 days. Unfortunately, only one set of ages (ages 1 year old, 1 year old and 36 years old) has a sum greater than 31, which leaves many possible combinations open as possible. For today’s date, the 13th, ages of 2, 2, and 9 would produce 36 and have a sum of 13, but, again, it is uncertain. If it were the first of the month, there would be no possible combinations that would produce 36 and sum 1.

24. Two candles of equal length were lit at the same time. One candle took 6 hr to burn out and the other candle took 3 hr to burn out. After how much time was one candle exactly twice as long as the other candle?

Answer: 2 hours.

Solution: The faster burning candle took half the time to burn as the slower burning candle (3 hours/ 6 hours = 1/2), meaning it burned twice as fast. This means that after 2/3 of the total burning time for the faster burning candle it will be 1/3 of its original height and at the slower burning candle will be at 2/3 of its original height and 1/3 is half of 2/3. Since the faster burning candle took 3 hours to burn, 2/3 of its total burning time is 2 hours.

25. Two candles of length L and L + 1 were lit at 6:00 and 4:30, respectively. At 8:30 they had the same length. The longer candle died at 10:30 and the shorter candle died at 10:00. Find L.

Answer: L=2.

Solution: The shorter candle lasted for 4 hours and the longer candle lasted for 6 hours. As 6 hours – 4 hours = 2 hours and 2 hours / 4 hours = 1/2, the longer candle lasted 50% longer and was, therefore, 50% longer in length. This means that the +1 in L+1 on the longer candle was 1/2 of L. 1/2L=1, so L=2*1, L=2.

Course:MATH110/Archive/2010-2011/003/Groups/Group 18

2010-11-12T05:21:52Z

RolandWill: /* 1-5 */

{{Infobox MATH110 Groups
| group number = 18
| member 1 = [[User:ChouJuChen|Audrey Chen]]
| member 2 = [[User:SifatHasan|Sifat Hasan]]
| member 3 = [[User:CaitlinLastiwkaFarquharson|Caitlin Lastiwka-Farquharson]]
| member 4 = [[User:VictoriaWall|Victoria Wall]]
| member 5 = [[User:RolandWill|Roland Will]]
| member 6 =
}}

==Sub-Pages==

Basic Skills Project [http://wiki.ubc.ca/Course:MATH110/003/Groups/Group_18/Basic_Skills_Project]

==Homework due October 20th, 2010==

I created a page for our homework due tomorrow: [http://wiki.ubc.ca/Course:MATH110/003/Groups/Group_18/Homework_October_20th,_2010 http://wiki.ubc.ca/Course:MATH110/003/Groups/Group 18/Homework October 20th, 2010]

-Roland

I've moved the page, it was missing the ''Course:'' part which means it was created directly inside the wiki and not as a subpage of your group page, which is something the wiki admins don't like that much. By the way, you're allowed to use spaces in the name of your pages.

-- [[User:DavidKohler|DavidKohler]] 06:28, 20 October 2010 (UTC)

1-5

==Victoria Wall ==
==1.A bus traveled from the terminal to the airport at an average speed of 30 mi/hr and the trip took an hour and 20 min. The bus then traveled from the airport back to the terminal and again averaged 30 mi/hr. However, the return trip required 80 min. Explain.==

' 'Lets call the terminal T and the airport A. If the bus travelled from T to A at 30mi/hr and it took them one hour and 20 mins to get from T to A at this speed, and there are 60 minutes in one hour, it took the bus 60min + 20min to get to A which is a total of 80min. The bus took 80 min to get from T to A. To get from A to T at the same speed (30mi/hr) it took the bus 80min. 80min = 80 min. This means going from A to T or vis versa at 30 mi/hr it will take the bus 80min.

==2.A lady did not have her driver's license with her when she failed to stop at a stop sign and then went three blocks down a one-way street the wrong way. A policeman saw her, but he did not stop her. Explain. ==

' 'The lady was walking. It never says she was driving.

==3.One of three boxes contains apples, another box contains oranges, and another box contains a mixture of apples and oranges. The boxes are labeled APPLES, ORANGES and APPLES AND ORANGES, but each label is incorrect. Can you select one fruit from only one box and determine the correct labels? Explain. ==

' 'if you selecet from the box APPLES AND ORANGES then you will be able to see the labels if they are correct or not.

==4.I am the brother of the blind fiddler, but brothers I have none. How can this be? ==

' 'Since it says that he is the brother of the blind fiddler it does not mean that the fiddle is male, since he has no brothers than the fiddler must be a female.

==5.Two quarters rest next to each other on a table. One coin is held fixed while the second coin is rolled around the edge of the first coin with no slipping. When the moving coin returns to its original position, how many times has it revolved? ==

' 'This is because the moving quarters revolves two full revolutions

==6-10==
== Caitlin Lastiwka- Farquharson ==

==6. Three kinds of apples are all mixed up in a basket. How many apples must you draw without (without looking) from the basket to be sure of getting at least two of a kind? ==

' ' To be sure you are getting at least two of a kind, you must select all of the other types of apples, plus two more. Meaning that only once you have selected all of the other apples can you be sure that you will select two of the kind you desire. It can be written like this: x,a x2, b and x3, c, with x representing the quantity of apples. This can be calculated by x2 + x3 +2. X2 representing one of the types of apples, x3 representing the other type and 2 representing 2 of the kind of apples you are trying to select. This is the only way to be sure you are getting at least two of a kind. ' '

==7. Suppose you have 40 blue socks and 40 brown socks in a drawer. How many socks must you take from the drawer (without looking) to be sure of getting (i) a pair of the same colour, and (ii) a pair with different colors. ==

' 'You must take three socks from the drawer to ensure you have a pair that match. This is because if you only select two, one could be brown and one could be blue. Selecting three, ensures that at least two of them will be the same colour. As for part two, you would need to select 41 socks to ensure you had a pair of different coloured socks because if you select 40 or less you could get all the same colour, but selecting 41 ensures you will have at least one pair of mixed colour. ' '

==8. Rueben says "Two days ago I was 20 years old. Later next year I will be 23 years old." Explain how this is possible. ==

' 'It is possible if your birthday is on the 31st of December and today is the 1st of January. This is because on the 30th of December (two days ago) you we’re 20 years old and now you are 21, later this year you will turn 22 on the 31st of December, and therefore 23 the next year.' '

==9. A rope ladder hanging over the side of a boat has rungs one foot apart. Ten rungs are showing. If the tide rises five feet, how many rungs will be showing? ==

' ' 5 rungs will be showing, because if there are 10 showing now, and they are each a foot apart, then for 5 more rungs to be showing there would need to be an increase in the level of water by 5 feet. ' '

==10.Suppose one-half of all people are chocolate eaters and one-half of all people are women. (i) Does it follow that one-fourth of all people are women chocolate eaters? (ii) Does it follow that one-half of all men are chocolate eaters? Explain. ==

' ' No, it does not follow that one-fourth of all people are women chocolate eaters and it does not follow that half of all men are chocolate eaters because are completely independent scenarios. Meaning that the the amount of women there are does not influence the amount of men that will eat chocolate. For example, If 50% of people are women and 50% of the entire population including men and women eat chocolate (arrived at by using the same logic that if 1/4 of women eat chocolate and 1/4 of men eat chocolate), that entire 50% could be comprised of women, meaning that no men eat chocolate disproving the statement.

==11-14==
==Sifat Hasan==

==11 11. A woman, her older brother, her son, and her daughter are chess players. The worst player’s twin, who is one of the four players, and the best player are of opposite sex. The worst player and the best player have the same age. If this is possible, who is the worst player?==

The four players (according to age, from oldest to youngest) are: woman's older brother, woman, and the son and the daughter (of the same age). Assuming that the children are of the same age (i.e. twins), the worst player is one of them, since they are the only ones who can have a twin. Assuming that the worst player is the daughter, her brother the son, is of the opposite sex as the woman, therefore the woman is the worst player. However, since the worst and the best player are of the same age, this is not possible, because the twins are of the opposite sex and they are of different genders.

==12 A Manhattan fellow had a girlfriend in the Bronx and a girlfriend in Brooklyn. He decided which girlfriend to visit by arriving randomly at the train station and taking the first of the Bronx or Brooklyn trains that arrived. The trains to Brooklyn and the Bronx each arrived regularly every 10 minutes. Not long after he began his scheme the man's Bronx girlfriend left him because he rarely visited. Give a (logical) explanation==

Assuming that the Bronx and the Brooklyn train arrive one after the other every 10 minutes, the only logical explanation would be that the man in Manhattan coincidentally went to the station 10 minutes or less before a train to Brooklyn arrived, most of the time.

==13 If a clock takes 5 seconds to strike 5:00 (with 5 equally spaced chimes), how long does it take to strike 10:00 (with 10 equally spaced chimes)?==

If it takes 5 seconds to strike 5, there will be 4 little halts in the middle. Therefore it takes 5 chimes 4 (5/4) = 1.25 second halts to finish. For 10 chimes, there are 9 halts so, it takes 9x 1.25 = 11.25 seconds for 10 halts.

==14 One day in the maternity ward, the name tags for four girl babies became mixed up. (i) In how many different ways could two of the babies be tagged correctly and two of the babies be tagged incorrectly? (ii) In how many different ways could three of the babies be tagged correctly and one baby be tagged incorrectly?==

(i)and (ii) If we take the babies names as A,B,C and D. There are 6 different combinations of the mix up, that two babies' names can be correct and 2 can be wrong. Assuming the name tags for the babies A,B,C and D are in respective order, they are ABDC, ADCB, ACBD, DBCA, CBAD and BACD. All other combinations for example BCAD will have one correct and 3 incorrect, or all four of them correct, because if 3 are correct, the fourth one has to be correct.

==15-16==
==Roland Will==

==15. Alex says to you, “I'll bet you any amount of money that if I shuffle this deck of cards, there will always be as many red cards in the first half of the deck as there are black cards in the second half of the deck.” Should you accept his bet?==

Answer: No, you shouldn't assuming the deck has equal amounts of red and black cards as in a standard 52 card deck.
Solution: In a standard 52 card deck, half of the cards (26) are black and half are red. If you take 26 cards at random from the deck, x of them will be black and y of them will be red, and x+y=26. As there are 26 of each color in the deck, then x+?=26 for the black cards in the deck and ?+y=26 for the red cards in the deck. As x+y=26 in the first randomly selected 26 cards, then the value of black cards in the other half of the deck must equal y, and the value of red cards in the other half of the deck must equal x meaning that "there will always be as many red cards in the first half of the deck as there are black cards in the second half of the deck."

==16. Suppose that each daughter in your family has the same number of brothers as she has sisters, and each son in your family has twice as many sisters as he has brothers. How many sons and daughters are in the family?==

Answer:3 total, 2 sister and 1 brother
Solution: Since the daughters in the family each have as many brothers as sisters the amount of sisters, with x standing for the amount of brothers, is x+1. As each brother has twice as many sisters as brothers, the amount of sisters must equal 2(x-1) or 2x-2. To find the number of brother: x+1=2x+1, 1=x-2, 3=x, which means that their are 3 brothers and 4 sisters (x+1= the number of sisters and x=3). This makes sense because a sister would have an equal amount of brothers to sisters, 3 sisters and 3 brothers, if there were 4 sisters and 3 brothers total, and each brother would have 4 sisters and 3 brothers, which is twice the amount of brothers to sisters.

==17~21==
==Audrey Chen==

==17.The zero point on a bathroom scale is set incorrectly, but otherwise the scale is accurate. It shows 60 kg when Dan stands on the scale, 50 kg when Sarah stands on the scale, but 105 kg when Dan and Sarah both stand on the scale. Does the scale read too high or too low? Explain. ==

''The scale read too low, since Dan is shown as 60kg and Sarah is 50kg, suppose 60+50=110, 105-110=-5, so that means the scale is smaller than 0 in the beginning''

==18. Alice takes one-third of the pennies from a large jar. Then Bret takes one-third of the remaining pennies from the jar. Finally, Carla takes one-third of the remaining pennies from the jar, leaving 40 pennies in the jar. How many pennies were in the jar at the start? ==

''If the total pennies is "x", Alice take 1/3x, so it has 2/3x left after Alice took it, than Bret take 1/3 out, after Alice took it, which is 2/3x*1/3= 2/9x, so in the beginning they have x, after Alice took it, it has 2/3x left, and Bret took 2/9x, so after Bret took it, it becomes 2/3x-2/9x= 4/9x-2/9x=2/9x left in the jar. Than Carla take 1/3 of the rest, so she took 1/3 of rest which is 2/9x*1/3=3/27x, so Alice took 1/3x, Bret tool 2/9x, Carla took 3/27x, three of them totaly took 1/3x+2/9x+3/27x=18/27x, so there still has x-18/27x= 9/27x= 1/3 left, 1/3x=40pennies, so x=120 pennies, so it was having 120 pennies in the jar.

==19. One morning each member of Angela's family drank an eight-ounce cup of coffee and milk, with the (nonzero) amounts of coffee and milk varying from cup to cup. Angela drank a quarter of the total amount of milk and a sixth of the total amount of coffee. What is the least number of people in the family? ==

''If we let total milk is x, total coffee is y. Than 1/4x+1/6y=8, and because every cup is 8ounce, x+y is multiple by 8. So make it easier, we use 1/4x+1/6y=8 * 12 to both sides. than we will got 3x+2y=96, now we have 3x+2y=96 and x+y is multiple of 8, and the number that multiple by 8 is 8, 16, 24, 32... so 2x+2y= 16, 32, 48, 64, 80, 96, since 3x+2y=96, it can't be more than 96. It will only have 6 possible number, so if you take 3x+2y=96 substracting 2x+2y=16, 32, 48, 64, 80, 96 you can get 6 possible x, which are 80, 64, 48, 32, 16, and 0. Than put the number into 3x+2y=96, if you put 80 in, will get 20, which is bigger than 8, and also 64, 48. If we use 32, it will equal to 8, but that means we have 0 coffee, but coffee can't be 0, so there's only 16 and 0 left. Since Angela had 1/4 of total amount of milk, milk can't be 0. So we got 16ounce than 16*(1/4)=4, so that means she had 8-4=4 's coffee. So 4=1/6 coffee, than the total amount of coffee would be 4*6=24. than x=16 and y=24, 16+24=40 40/8ounce=5, so at least have 5 cups of drinks, so that means at least they have 5 members in Angela's family.''

==20.Of two clocks next to each other, one runs 5 min per hour fast and the other runs 5 min per hour slow. At midnight the clocks show the same time. At what time are they are one hour apart? ==

''Since one clock runs 5 min faster per hour, the other is 5 min slower, after clock runs an hour, two clocks will have 10 min different from each other. 60 min an hour. 60/10=6, so after 6 hours two clocks will having one hour apart, and that would be 6AM.''

==21.Sven placed exactly in the middle among all runners in a race. Dan was slower than Sven, in 10th place, and Lars was in 16th place. How many runners were in the race? ==

''There were 17 runners. Since lars was in 16th place, the runners at least have to be 16, than if Sven is placed exactly in the middle, it means it would have even number of runners. Because Dan is slower and he was at 10 place that tells us Seven has to be before 10th, and if there has 19 runners, Sven and Dan would be at the same place, so it should be 17 runners, than Sven would be at exactly in the middle which at 9th place.''

==22-25==

Roland Will

22. During a vacation, it rained on 13 days, but when it rained in the morning, the afternoon was sunny, and every rainy afternoon was preceded by a sunny morning. There were 11 sunny mornings and 12 sunny afternoons. How long was the vacation?

Answer: 18 days of vacation.

Solution: 13 of the days of vacation were half sunny and half rainy. As there were 23 sunny mornings and afternoons (11 sunny mornings+12 sunny afternoons = 23 sunny mornings and afternoons), 13 of those sunny afternoons or mornings were on half rainy days. This means there are 10 sunny half-days left over, which equal 5 sunny full days. The 5 sunny full days plus the 13 half sunny/rainy days equal 18 total days of vacation.

23. Suppose you overhear the following conversation: Paul: How old are your three children? Paula: The product of their ages is 36 and the sum of their ages is the same as today's date. Paul: That is not enough information. Paula: The oldest child also has red hair. If you were Paul could you determine the ages of Paula's children? Explain.

Answer: If I were Paul this might be possible, but since we don’t know the date that Paula said this, it is not possible for us to find out.

Solution: There are many different combinations of three numbers that can be multiplied and will produce 36. As we do not know the date that Paula said this, the only thing we can be sure of is that the sum of the ages is less than 31 because no month has more than 31 days. Unfortunately, only one set of ages (ages 1 year old, 1 year old and 36 years old) has a sum greater than 31, which leaves many possible combinations open as possible. For today’s date, the 13th, ages of 2, 2, and 9 would produce 36 and have a sum of 13, but, again, it is uncertain. If it were the first of the month, there would be no possible combinations that would produce 36 and sum 1.

24. Two candles of equal length were lit at the same time. One candle took 6 hr to burn out and the other candle took 3 hr to burn out. After how much time was one candle exactly twice as long as the other candle?

Answer: 2 hours.

Solution: The faster burning candle took half the time to burn as the slower burning candle (3 hours/ 6 hours = 1/2), meaning it burned twice as fast. This means that after 2/3 of the total burning time for the faster burning candle it will be 1/3 of its original height and at the slower burning candle will be at 2/3 of its original height and 1/3 is half of 2/3. Since the faster burning candle took 3 hours to burn, 2/3 of its total burning time is 2 hours.

25. Two candles of length L and L + 1 were lit at 6:00 and 4:30, respectively. At 8:30 they had the same length. The longer candle died at 10:30 and the shorter candle died at 10:00. Find L.

Answer: L=2.

Solution: The shorter candle lasted for 4 hours and the longer candle lasted for 6 hours. As 6 hours – 4 hours = 2 hours and 2 hours / 4 hours = 1/2, the longer candle lasted 50% longer and was, therefore, 50% longer in length. This means that the +1 in L+1 on the longer candle was 1/2 of L. 1/2L=1, so L=2*1, L=2.

Course:MATH110/Archive/2010-2011/003/Groups/Group 18

2010-11-12T05:21:28Z

RolandWill: /* Homework due October 20th, 2010 */

{{Infobox MATH110 Groups
| group number = 18
| member 1 = [[User:ChouJuChen|Audrey Chen]]
| member 2 = [[User:SifatHasan|Sifat Hasan]]
| member 3 = [[User:CaitlinLastiwkaFarquharson|Caitlin Lastiwka-Farquharson]]
| member 4 = [[User:VictoriaWall|Victoria Wall]]
| member 5 = [[User:RolandWill|Roland Will]]
| member 6 =
}}

==Sub-Pages==

Basic Skills Project [http://wiki.ubc.ca/Course:MATH110/003/Groups/Group_18/Basic_Skills_Project]

==Homework due October 20th, 2010==

I created a page for our homework due tomorrow: [http://wiki.ubc.ca/Course:MATH110/003/Groups/Group_18/Homework_October_20th,_2010 http://wiki.ubc.ca/Course:MATH110/003/Groups/Group 18/Homework October 20th, 2010]

-Roland

I've moved the page, it was missing the ''Course:'' part which means it was created directly inside the wiki and not as a subpage of your group page, which is something the wiki admins don't like that much. By the way, you're allowed to use spaces in the name of your pages.

-- [[User:DavidKohler|DavidKohler]] 06:28, 20 October 2010 (UTC)

==1-5==
==Victoria Wall ==
==1.A bus traveled from the terminal to the airport at an average speed of 30 mi/hr and the trip took an hour and 20 min. The bus then traveled from the airport back to the terminal and again averaged 30 mi/hr. However, the return trip required 80 min. Explain.==

' 'Lets call the terminal T and the airport A. If the bus travelled from T to A at 30mi/hr and it took them one hour and 20 mins to get from T to A at this speed, and there are 60 minutes in one hour, it took the bus 60min + 20min to get to A which is a total of 80min. The bus took 80 min to get from T to A. To get from A to T at the same speed (30mi/hr) it took the bus 80min. 80min = 80 min. This means going from A to T or vis versa at 30 mi/hr it will take the bus 80min.

==2.A lady did not have her driver's license with her when she failed to stop at a stop sign and then went three blocks down a one-way street the wrong way. A policeman saw her, but he did not stop her. Explain. ==

' 'The lady was walking. It never says she was driving.

==3.One of three boxes contains apples, another box contains oranges, and another box contains a mixture of apples and oranges. The boxes are labeled APPLES, ORANGES and APPLES AND ORANGES, but each label is incorrect. Can you select one fruit from only one box and determine the correct labels? Explain. ==

' 'if you selecet from the box APPLES AND ORANGES then you will be able to see the labels if they are correct or not.

==4.I am the brother of the blind fiddler, but brothers I have none. How can this be? ==

' 'Since it says that he is the brother of the blind fiddler it does not mean that the fiddle is male, since he has no brothers than the fiddler must be a female.

==5.Two quarters rest next to each other on a table. One coin is held fixed while the second coin is rolled around the edge of the first coin with no slipping. When the moving coin returns to its original position, how many times has it revolved? ==

' 'This is because the moving quarters revolves two full revolutions

==6-10==
== Caitlin Lastiwka- Farquharson ==

==6. Three kinds of apples are all mixed up in a basket. How many apples must you draw without (without looking) from the basket to be sure of getting at least two of a kind? ==

' ' To be sure you are getting at least two of a kind, you must select all of the other types of apples, plus two more. Meaning that only once you have selected all of the other apples can you be sure that you will select two of the kind you desire. It can be written like this: x,a x2, b and x3, c, with x representing the quantity of apples. This can be calculated by x2 + x3 +2. X2 representing one of the types of apples, x3 representing the other type and 2 representing 2 of the kind of apples you are trying to select. This is the only way to be sure you are getting at least two of a kind. ' '

==7. Suppose you have 40 blue socks and 40 brown socks in a drawer. How many socks must you take from the drawer (without looking) to be sure of getting (i) a pair of the same colour, and (ii) a pair with different colors. ==

' 'You must take three socks from the drawer to ensure you have a pair that match. This is because if you only select two, one could be brown and one could be blue. Selecting three, ensures that at least two of them will be the same colour. As for part two, you would need to select 41 socks to ensure you had a pair of different coloured socks because if you select 40 or less you could get all the same colour, but selecting 41 ensures you will have at least one pair of mixed colour. ' '

==8. Rueben says "Two days ago I was 20 years old. Later next year I will be 23 years old." Explain how this is possible. ==

' 'It is possible if your birthday is on the 31st of December and today is the 1st of January. This is because on the 30th of December (two days ago) you we’re 20 years old and now you are 21, later this year you will turn 22 on the 31st of December, and therefore 23 the next year.' '

==9. A rope ladder hanging over the side of a boat has rungs one foot apart. Ten rungs are showing. If the tide rises five feet, how many rungs will be showing? ==

' ' 5 rungs will be showing, because if there are 10 showing now, and they are each a foot apart, then for 5 more rungs to be showing there would need to be an increase in the level of water by 5 feet. ' '

==10.Suppose one-half of all people are chocolate eaters and one-half of all people are women. (i) Does it follow that one-fourth of all people are women chocolate eaters? (ii) Does it follow that one-half of all men are chocolate eaters? Explain. ==

' ' No, it does not follow that one-fourth of all people are women chocolate eaters and it does not follow that half of all men are chocolate eaters because are completely independent scenarios. Meaning that the the amount of women there are does not influence the amount of men that will eat chocolate. For example, If 50% of people are women and 50% of the entire population including men and women eat chocolate (arrived at by using the same logic that if 1/4 of women eat chocolate and 1/4 of men eat chocolate), that entire 50% could be comprised of women, meaning that no men eat chocolate disproving the statement.

==11-14==
==Sifat Hasan==

==11 11. A woman, her older brother, her son, and her daughter are chess players. The worst player’s twin, who is one of the four players, and the best player are of opposite sex. The worst player and the best player have the same age. If this is possible, who is the worst player?==

The four players (according to age, from oldest to youngest) are: woman's older brother, woman, and the son and the daughter (of the same age). Assuming that the children are of the same age (i.e. twins), the worst player is one of them, since they are the only ones who can have a twin. Assuming that the worst player is the daughter, her brother the son, is of the opposite sex as the woman, therefore the woman is the worst player. However, since the worst and the best player are of the same age, this is not possible, because the twins are of the opposite sex and they are of different genders.

==12 A Manhattan fellow had a girlfriend in the Bronx and a girlfriend in Brooklyn. He decided which girlfriend to visit by arriving randomly at the train station and taking the first of the Bronx or Brooklyn trains that arrived. The trains to Brooklyn and the Bronx each arrived regularly every 10 minutes. Not long after he began his scheme the man's Bronx girlfriend left him because he rarely visited. Give a (logical) explanation==

Assuming that the Bronx and the Brooklyn train arrive one after the other every 10 minutes, the only logical explanation would be that the man in Manhattan coincidentally went to the station 10 minutes or less before a train to Brooklyn arrived, most of the time.

==13 If a clock takes 5 seconds to strike 5:00 (with 5 equally spaced chimes), how long does it take to strike 10:00 (with 10 equally spaced chimes)?==

If it takes 5 seconds to strike 5, there will be 4 little halts in the middle. Therefore it takes 5 chimes 4 (5/4) = 1.25 second halts to finish. For 10 chimes, there are 9 halts so, it takes 9x 1.25 = 11.25 seconds for 10 halts.

==14 One day in the maternity ward, the name tags for four girl babies became mixed up. (i) In how many different ways could two of the babies be tagged correctly and two of the babies be tagged incorrectly? (ii) In how many different ways could three of the babies be tagged correctly and one baby be tagged incorrectly?==

(i)and (ii) If we take the babies names as A,B,C and D. There are 6 different combinations of the mix up, that two babies' names can be correct and 2 can be wrong. Assuming the name tags for the babies A,B,C and D are in respective order, they are ABDC, ADCB, ACBD, DBCA, CBAD and BACD. All other combinations for example BCAD will have one correct and 3 incorrect, or all four of them correct, because if 3 are correct, the fourth one has to be correct.

==15-16==
==Roland Will==

==15. Alex says to you, “I'll bet you any amount of money that if I shuffle this deck of cards, there will always be as many red cards in the first half of the deck as there are black cards in the second half of the deck.” Should you accept his bet?==

Answer: No, you shouldn't assuming the deck has equal amounts of red and black cards as in a standard 52 card deck.
Solution: In a standard 52 card deck, half of the cards (26) are black and half are red. If you take 26 cards at random from the deck, x of them will be black and y of them will be red, and x+y=26. As there are 26 of each color in the deck, then x+?=26 for the black cards in the deck and ?+y=26 for the red cards in the deck. As x+y=26 in the first randomly selected 26 cards, then the value of black cards in the other half of the deck must equal y, and the value of red cards in the other half of the deck must equal x meaning that "there will always be as many red cards in the first half of the deck as there are black cards in the second half of the deck."

==16. Suppose that each daughter in your family has the same number of brothers as she has sisters, and each son in your family has twice as many sisters as he has brothers. How many sons and daughters are in the family?==

Answer:3 total, 2 sister and 1 brother
Solution: Since the daughters in the family each have as many brothers as sisters the amount of sisters, with x standing for the amount of brothers, is x+1. As each brother has twice as many sisters as brothers, the amount of sisters must equal 2(x-1) or 2x-2. To find the number of brother: x+1=2x+1, 1=x-2, 3=x, which means that their are 3 brothers and 4 sisters (x+1= the number of sisters and x=3). This makes sense because a sister would have an equal amount of brothers to sisters, 3 sisters and 3 brothers, if there were 4 sisters and 3 brothers total, and each brother would have 4 sisters and 3 brothers, which is twice the amount of brothers to sisters.

==17~21==
==Audrey Chen==

==17.The zero point on a bathroom scale is set incorrectly, but otherwise the scale is accurate. It shows 60 kg when Dan stands on the scale, 50 kg when Sarah stands on the scale, but 105 kg when Dan and Sarah both stand on the scale. Does the scale read too high or too low? Explain. ==

''The scale read too low, since Dan is shown as 60kg and Sarah is 50kg, suppose 60+50=110, 105-110=-5, so that means the scale is smaller than 0 in the beginning''

==18. Alice takes one-third of the pennies from a large jar. Then Bret takes one-third of the remaining pennies from the jar. Finally, Carla takes one-third of the remaining pennies from the jar, leaving 40 pennies in the jar. How many pennies were in the jar at the start? ==

''If the total pennies is "x", Alice take 1/3x, so it has 2/3x left after Alice took it, than Bret take 1/3 out, after Alice took it, which is 2/3x*1/3= 2/9x, so in the beginning they have x, after Alice took it, it has 2/3x left, and Bret took 2/9x, so after Bret took it, it becomes 2/3x-2/9x= 4/9x-2/9x=2/9x left in the jar. Than Carla take 1/3 of the rest, so she took 1/3 of rest which is 2/9x*1/3=3/27x, so Alice took 1/3x, Bret tool 2/9x, Carla took 3/27x, three of them totaly took 1/3x+2/9x+3/27x=18/27x, so there still has x-18/27x= 9/27x= 1/3 left, 1/3x=40pennies, so x=120 pennies, so it was having 120 pennies in the jar.

==19. One morning each member of Angela's family drank an eight-ounce cup of coffee and milk, with the (nonzero) amounts of coffee and milk varying from cup to cup. Angela drank a quarter of the total amount of milk and a sixth of the total amount of coffee. What is the least number of people in the family? ==

''If we let total milk is x, total coffee is y. Than 1/4x+1/6y=8, and because every cup is 8ounce, x+y is multiple by 8. So make it easier, we use 1/4x+1/6y=8 * 12 to both sides. than we will got 3x+2y=96, now we have 3x+2y=96 and x+y is multiple of 8, and the number that multiple by 8 is 8, 16, 24, 32... so 2x+2y= 16, 32, 48, 64, 80, 96, since 3x+2y=96, it can't be more than 96. It will only have 6 possible number, so if you take 3x+2y=96 substracting 2x+2y=16, 32, 48, 64, 80, 96 you can get 6 possible x, which are 80, 64, 48, 32, 16, and 0. Than put the number into 3x+2y=96, if you put 80 in, will get 20, which is bigger than 8, and also 64, 48. If we use 32, it will equal to 8, but that means we have 0 coffee, but coffee can't be 0, so there's only 16 and 0 left. Since Angela had 1/4 of total amount of milk, milk can't be 0. So we got 16ounce than 16*(1/4)=4, so that means she had 8-4=4 's coffee. So 4=1/6 coffee, than the total amount of coffee would be 4*6=24. than x=16 and y=24, 16+24=40 40/8ounce=5, so at least have 5 cups of drinks, so that means at least they have 5 members in Angela's family.''

==20.Of two clocks next to each other, one runs 5 min per hour fast and the other runs 5 min per hour slow. At midnight the clocks show the same time. At what time are they are one hour apart? ==

''Since one clock runs 5 min faster per hour, the other is 5 min slower, after clock runs an hour, two clocks will have 10 min different from each other. 60 min an hour. 60/10=6, so after 6 hours two clocks will having one hour apart, and that would be 6AM.''

==21.Sven placed exactly in the middle among all runners in a race. Dan was slower than Sven, in 10th place, and Lars was in 16th place. How many runners were in the race? ==

''There were 17 runners. Since lars was in 16th place, the runners at least have to be 16, than if Sven is placed exactly in the middle, it means it would have even number of runners. Because Dan is slower and he was at 10 place that tells us Seven has to be before 10th, and if there has 19 runners, Sven and Dan would be at the same place, so it should be 17 runners, than Sven would be at exactly in the middle which at 9th place.''

==22-25==

Roland Will

22. During a vacation, it rained on 13 days, but when it rained in the morning, the afternoon was sunny, and every rainy afternoon was preceded by a sunny morning. There were 11 sunny mornings and 12 sunny afternoons. How long was the vacation?

Answer: 18 days of vacation.

Solution: 13 of the days of vacation were half sunny and half rainy. As there were 23 sunny mornings and afternoons (11 sunny mornings+12 sunny afternoons = 23 sunny mornings and afternoons), 13 of those sunny afternoons or mornings were on half rainy days. This means there are 10 sunny half-days left over, which equal 5 sunny full days. The 5 sunny full days plus the 13 half sunny/rainy days equal 18 total days of vacation.

23. Suppose you overhear the following conversation: Paul: How old are your three children? Paula: The product of their ages is 36 and the sum of their ages is the same as today's date. Paul: That is not enough information. Paula: The oldest child also has red hair. If you were Paul could you determine the ages of Paula's children? Explain.

Answer: If I were Paul this might be possible, but since we don’t know the date that Paula said this, it is not possible for us to find out.

Solution: There are many different combinations of three numbers that can be multiplied and will produce 36. As we do not know the date that Paula said this, the only thing we can be sure of is that the sum of the ages is less than 31 because no month has more than 31 days. Unfortunately, only one set of ages (ages 1 year old, 1 year old and 36 years old) has a sum greater than 31, which leaves many possible combinations open as possible. For today’s date, the 13th, ages of 2, 2, and 9 would produce 36 and have a sum of 13, but, again, it is uncertain. If it were the first of the month, there would be no possible combinations that would produce 36 and sum 1.

24. Two candles of equal length were lit at the same time. One candle took 6 hr to burn out and the other candle took 3 hr to burn out. After how much time was one candle exactly twice as long as the other candle?

Answer: 2 hours.

Solution: The faster burning candle took half the time to burn as the slower burning candle (3 hours/ 6 hours = 1/2), meaning it burned twice as fast. This means that after 2/3 of the total burning time for the faster burning candle it will be 1/3 of its original height and at the slower burning candle will be at 2/3 of its original height and 1/3 is half of 2/3. Since the faster burning candle took 3 hours to burn, 2/3 of its total burning time is 2 hours.

25. Two candles of length L and L + 1 were lit at 6:00 and 4:30, respectively. At 8:30 they had the same length. The longer candle died at 10:30 and the shorter candle died at 10:00. Find L.

Answer: L=2.

Solution: The shorter candle lasted for 4 hours and the longer candle lasted for 6 hours. As 6 hours – 4 hours = 2 hours and 2 hours / 4 hours = 1/2, the longer candle lasted 50% longer and was, therefore, 50% longer in length. This means that the +1 in L+1 on the longer candle was 1/2 of L. 1/2L=1, so L=2*1, L=2.

Course:MATH110/Archive/2010-2011/003/Groups/Group 18

2010-10-29T07:58:51Z

RolandWill: /* 25. Two candles of length L and L + 1 were lit at 6:00 and 4:30, respectively. At 8:30 they had the same length. The longer candle died at 10:30 and the shorter candle died at 10:00. Find L. */

{{Infobox MATH110 Groups
| group number = 18
| member 1 = [[User:ChouJuChen|Audrey Chen]]
| member 2 = [[User:SifatHasan|Sifat Hasan]]
| member 3 = [[User:CaitlinLastiwkaFarquharson|Caitlin Lastiwka-Farquharson]]
| member 4 = [[User:VictoriaWall|Victoria Wall]]
| member 5 = [[User:RolandWill|Roland Will]]
| member 6 =
}}

==Homework due October 20th, 2010==

I created a page for our homework due tomorrow: [http://wiki.ubc.ca/Course:MATH110/003/Groups/Group_18/Homework_October_20th,_2010 http://wiki.ubc.ca/Course:MATH110/003/Groups/Group 18/Homework October 20th, 2010]

-Roland

I've moved the page, it was missing the ''Course:'' part which means it was created directly inside the wiki and not as a subpage of your group page, which is something the wiki admins don't like that much. By the way, you're allowed to use spaces in the name of your pages.

-- [[User:DavidKohler|DavidKohler]] 06:28, 20 October 2010 (UTC)

==1-5==
==Victoria Wall ==
==1.A bus traveled from the terminal to the airport at an average speed of 30 mi/hr and the trip took an hour and 20 min. The bus then traveled from the airport back to the terminal and again averaged 30 mi/hr. However, the return trip required 80 min. Explain.==

' 'Lets call the terminal T and the airport A. If the bus travelled from T to A at 30mi/hr and it took them one hour and 20 mins to get from T to A at this speed, and there are 60 minutes in one hour, it took the bus 60min + 20min to get to A which is a total of 80min. The bus took 80 min to get from T to A. To get from A to T at the same speed (30mi/hr) it took the bus 80min. 80min = 80 min. This means going from A to T or vis versa at 30 mi/hr it will take the bus 80min.

==2.A lady did not have her driver's license with her when she failed to stop at a stop sign and then went three blocks down a one-way street the wrong way. A policeman saw her, but he did not stop her. Explain. ==

' 'The lady was walking. It never says she was driving.

==3.One of three boxes contains apples, another box contains oranges, and another box contains a mixture of apples and oranges. The boxes are labeled APPLES, ORANGES and APPLES AND ORANGES, but each label is incorrect. Can you select one fruit from only one box and determine the correct labels? Explain. ==

' 'if you selecet from the box APPLES AND ORANGES then you will be able to see the labels if they are correct or not.

==4.I am the brother of the blind fiddler, but brothers I have none. How can this be? ==

' 'Since it says that he is the brother of the blind fiddler it does not mean that the fiddle is male, since he has no brothers than the fiddler must be a female.

==5.Two quarters rest next to each other on a table. One coin is held fixed while the second coin is rolled around the edge of the first coin with no slipping. When the moving coin returns to its original position, how many times has it revolved? ==

' 'This is because the moving quarters revolves two full revolutions

==6-10==
== Caitlin Lastiwka- Farquharson ==

==6. Three kinds of apples are all mixed up in a basket. How many apples must you draw without (without looking) from the basket to be sure of getting at least two of a kind? ==

' ' To be sure you are getting at least two of a kind, you must select all of the other types of apples, plus two more. Meaning that only once you have selected all of the other apples can you be sure that you will select two of the kind you desire. It can be written like this: x,a x2, b and x3, c, with x representing the quantity of apples. This can be calculated by x2 + x3 +2. X2 representing one of the types of apples, x3 representing the other type and 2 representing 2 of the kind of apples you are trying to select. This is the only way to be sure you are getting at least two of a kind. ' '

==7. Suppose you have 40 blue socks and 40 brown socks in a drawer. How many socks must you take from the drawer (without looking) to be sure of getting (i) a pair of the same colour, and (ii) a pair with different colors. ==

' 'You must take three socks from the drawer to ensure you have a pair that match. This is because if you only select two, one could be brown and one could be blue. Selecting three, ensures that at least two of them will be the same colour. As for part two, you would need to select 41 socks to ensure you had a pair of different coloured socks because if you select 40 or less you could get all the same colour, but selecting 41 ensures you will have at least one pair of mixed colour. ' '

==8. Rueben says "Two days ago I was 20 years old. Later next year I will be 23 years old." Explain how this is possible. ==

' 'It is possible if your birthday is on the 31st of December and today is the 1st of January. This is because on the 30th of December (two days ago) you we’re 20 years old and now you are 21, later this year you will turn 22 on the 31st of December, and therefore 23 the next year.' '

==9. A rope ladder hanging over the side of a boat has rungs one foot apart. Ten rungs are showing. If the tide rises five feet, how many rungs will be showing? ==

' ' 5 rungs will be showing, because if there are 10 showing now, and they are each a foot apart, then for 5 more rungs to be showing there would need to be an increase in the level of water by 5 feet. ' '

==10.Suppose one-half of all people are chocolate eaters and one-half of all people are women. (i) Does it follow that one-fourth of all people are women chocolate eaters? (ii) Does it follow that one-half of all men are chocolate eaters? Explain. ==

' ' No, it does not follow that one-fourth of all people are women chocolate eaters and it does not follow that half of all men are chocolate eaters because are completely independent scenarios. Meaning that the the amount of women there are does not influence the amount of men that will eat chocolate. For example, If 50% of people are women and 50% of the entire population including men and women eat chocolate (arrived at by using the same logic that if 1/4 of women eat chocolate and 1/4 of men eat chocolate), that entire 50% could be comprised of women, meaning that no men eat chocolate disproving the statement.

==11-14==
==Sifat Hasan==

==11 11. A woman, her older brother, her son, and her daughter are chess players. The worst player’s twin, who is one of the four players, and the best player are of opposite sex. The worst player and the best player have the same age. If this is possible, who is the worst player?==

The four players (according to age, from oldest to youngest) are: woman's older brother, woman, and the son and the daughter (of the same age). Assuming that the children are of the same age (i.e. twins), the worst player is one of them, since they are the only ones who can have a twin. Assuming that the worst player is the daughter, her brother the son, is of the opposite sex as the woman, therefore the woman is the worst player. However, since the worst and the best player are of the same age, this is not possible, because the twins are of the opposite sex and they are of different genders.

==12 A Manhattan fellow had a girlfriend in the Bronx and a girlfriend in Brooklyn. He decided which girlfriend to visit by arriving randomly at the train station and taking the first of the Bronx or Brooklyn trains that arrived. The trains to Brooklyn and the Bronx each arrived regularly every 10 minutes. Not long after he began his scheme the man's Bronx girlfriend left him because he rarely visited. Give a (logical) explanation==

Assuming that the Bronx and the Brooklyn train arrive one after the other every 10 minutes, the only logical explanation would be that the man in Manhattan coincidentally went to the station 10 minutes or less before a train to Brooklyn arrived, most of the time.

==13 If a clock takes 5 seconds to strike 5:00 (with 5 equally spaced chimes), how long does it take to strike 10:00 (with 10 equally spaced chimes)?==

If it takes 5 seconds to strike 5, there will be 4 little halts in the middle. Therefore it takes 5 chimes 4 (5/4) = 1.25 second halts to finish. For 10 chimes, there are 9 halts so, it takes 9x 1.25 = 11.25 seconds for 10 halts.

==14 One day in the maternity ward, the name tags for four girl babies became mixed up. (i) In how many different ways could two of the babies be tagged correctly and two of the babies be tagged incorrectly? (ii) In how many different ways could three of the babies be tagged correctly and one baby be tagged incorrectly?==

(i)and (ii) If we take the babies names as A,B,C and D. There are 6 different combinations of the mix up, that two babies' names can be correct and 2 can be wrong. Assuming the name tags for the babies A,B,C and D are in respective order, they are ABDC, ADCB, ACBD, DBCA, CBAD and BACD. All other combinations for example BCAD will have one correct and 3 incorrect, or all four of them correct, because if 3 are correct, the fourth one has to be correct.

==15-16==
==Roland Will==

==15. Alex says to you, “I'll bet you any amount of money that if I shuffle this deck of cards, there will always be as many red cards in the first half of the deck as there are black cards in the second half of the deck.” Should you accept his bet?==

Answer: No, you shouldn't assuming the deck has equal amounts of red and black cards as in a standard 52 card deck.
Solution: In a standard 52 card deck, half of the cards (26) are black and half are red. If you take 26 cards at random from the deck, x of them will be black and y of them will be red, and x+y=26. As there are 26 of each color in the deck, then x+?=26 for the black cards in the deck and ?+y=26 for the red cards in the deck. As x+y=26 in the first randomly selected 26 cards, then the value of black cards in the other half of the deck must equal y, and the value of red cards in the other half of the deck must equal x meaning that "there will always be as many red cards in the first half of the deck as there are black cards in the second half of the deck."

==16. Suppose that each daughter in your family has the same number of brothers as she has sisters, and each son in your family has twice as many sisters as he has brothers. How many sons and daughters are in the family?==

Answer:3 total, 2 sister and 1 brother
Solution: Since the daughters in the family each have as many brothers as sisters the amount of sisters, with x standing for the amount of brothers, is x+1. As each brother has twice as many sisters as brothers, the amount of sisters must equal 2(x-1) or 2x-2. To find the number of brother: x+1=2x+1, 1=x-2, 3=x, which means that their are 3 brothers and 4 sisters (x+1= the number of sisters and x=3). This makes sense because a sister would have an equal amount of brothers to sisters, 3 sisters and 3 brothers, if there were 4 sisters and 3 brothers total, and each brother would have 4 sisters and 3 brothers, which is twice the amount of brothers to sisters.

==17~21==
==Audrey Chen==

==17.The zero point on a bathroom scale is set incorrectly, but otherwise the scale is accurate. It shows 60 kg when Dan stands on the scale, 50 kg when Sarah stands on the scale, but 105 kg when Dan and Sarah both stand on the scale. Does the scale read too high or too low? Explain. ==

''The scale read too low, since Dan is shown as 60kg and Sarah is 50kg, suppose 60+50=110, 105-110=-5, so that means the scale is smaller than 0 in the beginning''

==18. Alice takes one-third of the pennies from a large jar. Then Bret takes one-third of the remaining pennies from the jar. Finally, Carla takes one-third of the remaining pennies from the jar, leaving 40 pennies in the jar. How many pennies were in the jar at the start? ==

''If the total pennies is "x", Alice take 1/3x, so it has 2/3x left after Alice took it, than Bret take 1/3 out, after Alice took it, which is 2/3x*1/3= 2/9x, so in the beginning they have x, after Alice took it, it has 2/3x left, and Bret took 2/9x, so after Bret took it, it becomes 2/3x-2/9x= 4/9x-2/9x=2/9x left in the jar. Than Carla take 1/3 of the rest, so she took 1/3 of rest which is 2/9x*1/3=3/27x, so Alice took 1/3x, Bret tool 2/9x, Carla took 3/27x, three of them totaly took 1/3x+2/9x+3/27x=18/27x, so there still has x-18/27x= 9/27x= 1/3 left, 1/3x=40pennies, so x=120 pennies, so it was having 120 pennies in the jar.

==19. One morning each member of Angela's family drank an eight-ounce cup of coffee and milk, with the (nonzero) amounts of coffee and milk varying from cup to cup. Angela drank a quarter of the total amount of milk and a sixth of the total amount of coffee. What is the least number of people in the family? ==

''If we let total milk is x, total coffee is y. Than 1/4x+1/6y=8, and because every cup is 8ounce, x+y is multiple by 8. So make it easier, we use 1/4x+1/6y=8 * 12 to both sides. than we will got 3x+2y=96, now we have 3x+2y=96 and x+y is multiple of 8, and the number that multiple by 8 is 8, 16, 24, 32... so 2x+2y= 16, 32, 48, 64, 80, 96, since 3x+2y=96, it can't be more than 96. It will only have 6 possible number, so if you take 3x+2y=96 substracting 2x+2y=16, 32, 48, 64, 80, 96 you can get 6 possible x, which are 80, 64, 48, 32, 16, and 0. Than put the number into 3x+2y=96, if you put 80 in, will get 20, which is bigger than 8, and also 64, 48. If we use 32, it will equal to 8, but that means we have 0 coffee, but coffee can't be 0, so there's only 16 and 0 left. Since Angela had 1/4 of total amount of milk, milk can't be 0. So we got 16ounce than 16*(1/4)=4, so that means she had 8-4=4 's coffee. So 4=1/6 coffee, than the total amount of coffee would be 4*6=24. than x=16 and y=24, 16+24=40 40/8ounce=5, so at least have 5 cups of drinks, so that means at least they have 5 members in Angela's family.''

==20.Of two clocks next to each other, one runs 5 min per hour fast and the other runs 5 min per hour slow. At midnight the clocks show the same time. At what time are they are one hour apart? ==

''Since one clock runs 5 min faster per hour, the other is 5 min slower, after clock runs an hour, two clocks will have 10 min different from each other. 60 min an hour. 60/10=6, so after 6 hours two clocks will having one hour apart, and that would be 6AM.''

==21.Sven placed exactly in the middle among all runners in a race. Dan was slower than Sven, in 10th place, and Lars was in 16th place. How many runners were in the race? ==

''There were 17 runners. Since lars was in 16th place, the runners at least have to be 16, than if Sven is placed exactly in the middle, it means it would have even number of runners. Because Dan is slower and he was at 10 place that tells us Seven has to be before 10th, and if there has 19 runners, Sven and Dan would be at the same place, so it should be 17 runners, than Sven would be at exactly in the middle which at 9th place.''

==22-25==

Roland Will

22. During a vacation, it rained on 13 days, but when it rained in the morning, the afternoon was sunny, and every rainy afternoon was preceded by a sunny morning. There were 11 sunny mornings and 12 sunny afternoons. How long was the vacation?

Answer: 18 days of vacation.

Solution: 13 of the days of vacation were half sunny and half rainy. As there were 23 sunny mornings and afternoons (11 sunny mornings+12 sunny afternoons = 23 sunny mornings and afternoons), 13 of those sunny afternoons or mornings were on half rainy days. This means there are 10 sunny half-days left over, which equal 5 sunny full days. The 5 sunny full days plus the 13 half sunny/rainy days equal 18 total days of vacation.

23. Suppose you overhear the following conversation: Paul: How old are your three children? Paula: The product of their ages is 36 and the sum of their ages is the same as today's date. Paul: That is not enough information. Paula: The oldest child also has red hair. If you were Paul could you determine the ages of Paula's children? Explain.

Answer: If I were Paul this might be possible, but since we don’t know the date that Paula said this, it is not possible for us to find out.

Solution: There are many different combinations of three numbers that can be multiplied and will produce 36. As we do not know the date that Paula said this, the only thing we can be sure of is that the sum of the ages is less than 31 because no month has more than 31 days. Unfortunately, only one set of ages (ages 1 year old, 1 year old and 36 years old) has a sum greater than 31, which leaves many possible combinations open as possible. For today’s date, the 13th, ages of 2, 2, and 9 would produce 36 and have a sum of 13, but, again, it is uncertain. If it were the first of the month, there would be no possible combinations that would produce 36 and sum 1.

24. Two candles of equal length were lit at the same time. One candle took 6 hr to burn out and the other candle took 3 hr to burn out. After how much time was one candle exactly twice as long as the other candle?

Answer: 2 hours.

Solution: The faster burning candle took half the time to burn as the slower burning candle (3 hours/ 6 hours = 1/2), meaning it burned twice as fast. This means that after 2/3 of the total burning time for the faster burning candle it will be 1/3 of its original height and at the slower burning candle will be at 2/3 of its original height and 1/3 is half of 2/3. Since the faster burning candle took 3 hours to burn, 2/3 of its total burning time is 2 hours.

25. Two candles of length L and L + 1 were lit at 6:00 and 4:30, respectively. At 8:30 they had the same length. The longer candle died at 10:30 and the shorter candle died at 10:00. Find L.

Answer: L=2.

Solution: The shorter candle lasted for 4 hours and the longer candle lasted for 6 hours. As 6 hours – 4 hours = 2 hours and 2 hours / 4 hours = 1/2, the longer candle lasted 50% longer and was, therefore, 50% longer in length. This means that the +1 in L+1 on the longer candle was 1/2 of L. 1/2L=1, so L=2*1, L=2.

Course:MATH110/Archive/2010-2011/003/Groups/Group 18

2010-10-29T07:58:35Z

RolandWill: /* 24. Two candles of equal length were lit at the same time. One candle took 6 hr to burn out and the other candle took 3 hr to burn out. After how much time was one candle exactly twice as long as the other candle? */

{{Infobox MATH110 Groups
| group number = 18
| member 1 = [[User:ChouJuChen|Audrey Chen]]
| member 2 = [[User:SifatHasan|Sifat Hasan]]
| member 3 = [[User:CaitlinLastiwkaFarquharson|Caitlin Lastiwka-Farquharson]]
| member 4 = [[User:VictoriaWall|Victoria Wall]]
| member 5 = [[User:RolandWill|Roland Will]]
| member 6 =
}}

==Homework due October 20th, 2010==

I created a page for our homework due tomorrow: [http://wiki.ubc.ca/Course:MATH110/003/Groups/Group_18/Homework_October_20th,_2010 http://wiki.ubc.ca/Course:MATH110/003/Groups/Group 18/Homework October 20th, 2010]

-Roland

I've moved the page, it was missing the ''Course:'' part which means it was created directly inside the wiki and not as a subpage of your group page, which is something the wiki admins don't like that much. By the way, you're allowed to use spaces in the name of your pages.

-- [[User:DavidKohler|DavidKohler]] 06:28, 20 October 2010 (UTC)

==1-5==
==Victoria Wall ==
==1.A bus traveled from the terminal to the airport at an average speed of 30 mi/hr and the trip took an hour and 20 min. The bus then traveled from the airport back to the terminal and again averaged 30 mi/hr. However, the return trip required 80 min. Explain.==

' 'Lets call the terminal T and the airport A. If the bus travelled from T to A at 30mi/hr and it took them one hour and 20 mins to get from T to A at this speed, and there are 60 minutes in one hour, it took the bus 60min + 20min to get to A which is a total of 80min. The bus took 80 min to get from T to A. To get from A to T at the same speed (30mi/hr) it took the bus 80min. 80min = 80 min. This means going from A to T or vis versa at 30 mi/hr it will take the bus 80min.

==2.A lady did not have her driver's license with her when she failed to stop at a stop sign and then went three blocks down a one-way street the wrong way. A policeman saw her, but he did not stop her. Explain. ==

' 'The lady was walking. It never says she was driving.

==3.One of three boxes contains apples, another box contains oranges, and another box contains a mixture of apples and oranges. The boxes are labeled APPLES, ORANGES and APPLES AND ORANGES, but each label is incorrect. Can you select one fruit from only one box and determine the correct labels? Explain. ==

' 'if you selecet from the box APPLES AND ORANGES then you will be able to see the labels if they are correct or not.

==4.I am the brother of the blind fiddler, but brothers I have none. How can this be? ==

' 'Since it says that he is the brother of the blind fiddler it does not mean that the fiddle is male, since he has no brothers than the fiddler must be a female.

==5.Two quarters rest next to each other on a table. One coin is held fixed while the second coin is rolled around the edge of the first coin with no slipping. When the moving coin returns to its original position, how many times has it revolved? ==

' 'This is because the moving quarters revolves two full revolutions

==6-10==
== Caitlin Lastiwka- Farquharson ==

==6. Three kinds of apples are all mixed up in a basket. How many apples must you draw without (without looking) from the basket to be sure of getting at least two of a kind? ==

' ' To be sure you are getting at least two of a kind, you must select all of the other types of apples, plus two more. Meaning that only once you have selected all of the other apples can you be sure that you will select two of the kind you desire. It can be written like this: x,a x2, b and x3, c, with x representing the quantity of apples. This can be calculated by x2 + x3 +2. X2 representing one of the types of apples, x3 representing the other type and 2 representing 2 of the kind of apples you are trying to select. This is the only way to be sure you are getting at least two of a kind. ' '

==7. Suppose you have 40 blue socks and 40 brown socks in a drawer. How many socks must you take from the drawer (without looking) to be sure of getting (i) a pair of the same colour, and (ii) a pair with different colors. ==

' 'You must take three socks from the drawer to ensure you have a pair that match. This is because if you only select two, one could be brown and one could be blue. Selecting three, ensures that at least two of them will be the same colour. As for part two, you would need to select 41 socks to ensure you had a pair of different coloured socks because if you select 40 or less you could get all the same colour, but selecting 41 ensures you will have at least one pair of mixed colour. ' '

==8. Rueben says "Two days ago I was 20 years old. Later next year I will be 23 years old." Explain how this is possible. ==

' 'It is possible if your birthday is on the 31st of December and today is the 1st of January. This is because on the 30th of December (two days ago) you we’re 20 years old and now you are 21, later this year you will turn 22 on the 31st of December, and therefore 23 the next year.' '

==9. A rope ladder hanging over the side of a boat has rungs one foot apart. Ten rungs are showing. If the tide rises five feet, how many rungs will be showing? ==

' ' 5 rungs will be showing, because if there are 10 showing now, and they are each a foot apart, then for 5 more rungs to be showing there would need to be an increase in the level of water by 5 feet. ' '

==10.Suppose one-half of all people are chocolate eaters and one-half of all people are women. (i) Does it follow that one-fourth of all people are women chocolate eaters? (ii) Does it follow that one-half of all men are chocolate eaters? Explain. ==

' ' No, it does not follow that one-fourth of all people are women chocolate eaters and it does not follow that half of all men are chocolate eaters because are completely independent scenarios. Meaning that the the amount of women there are does not influence the amount of men that will eat chocolate. For example, If 50% of people are women and 50% of the entire population including men and women eat chocolate (arrived at by using the same logic that if 1/4 of women eat chocolate and 1/4 of men eat chocolate), that entire 50% could be comprised of women, meaning that no men eat chocolate disproving the statement.

==11-14==
==Sifat Hasan==

==11 11. A woman, her older brother, her son, and her daughter are chess players. The worst player’s twin, who is one of the four players, and the best player are of opposite sex. The worst player and the best player have the same age. If this is possible, who is the worst player?==

The four players (according to age, from oldest to youngest) are: woman's older brother, woman, and the son and the daughter (of the same age). Assuming that the children are of the same age (i.e. twins), the worst player is one of them, since they are the only ones who can have a twin. Assuming that the worst player is the daughter, her brother the son, is of the opposite sex as the woman, therefore the woman is the worst player. However, since the worst and the best player are of the same age, this is not possible, because the twins are of the opposite sex and they are of different genders.

==12 A Manhattan fellow had a girlfriend in the Bronx and a girlfriend in Brooklyn. He decided which girlfriend to visit by arriving randomly at the train station and taking the first of the Bronx or Brooklyn trains that arrived. The trains to Brooklyn and the Bronx each arrived regularly every 10 minutes. Not long after he began his scheme the man's Bronx girlfriend left him because he rarely visited. Give a (logical) explanation==

Assuming that the Bronx and the Brooklyn train arrive one after the other every 10 minutes, the only logical explanation would be that the man in Manhattan coincidentally went to the station 10 minutes or less before a train to Brooklyn arrived, most of the time.

==13 If a clock takes 5 seconds to strike 5:00 (with 5 equally spaced chimes), how long does it take to strike 10:00 (with 10 equally spaced chimes)?==

If it takes 5 seconds to strike 5, there will be 4 little halts in the middle. Therefore it takes 5 chimes 4 (5/4) = 1.25 second halts to finish. For 10 chimes, there are 9 halts so, it takes 9x 1.25 = 11.25 seconds for 10 halts.

==14 One day in the maternity ward, the name tags for four girl babies became mixed up. (i) In how many different ways could two of the babies be tagged correctly and two of the babies be tagged incorrectly? (ii) In how many different ways could three of the babies be tagged correctly and one baby be tagged incorrectly?==

(i)and (ii) If we take the babies names as A,B,C and D. There are 6 different combinations of the mix up, that two babies' names can be correct and 2 can be wrong. Assuming the name tags for the babies A,B,C and D are in respective order, they are ABDC, ADCB, ACBD, DBCA, CBAD and BACD. All other combinations for example BCAD will have one correct and 3 incorrect, or all four of them correct, because if 3 are correct, the fourth one has to be correct.

==15-16==
==Roland Will==

==15. Alex says to you, “I'll bet you any amount of money that if I shuffle this deck of cards, there will always be as many red cards in the first half of the deck as there are black cards in the second half of the deck.” Should you accept his bet?==

Answer: No, you shouldn't assuming the deck has equal amounts of red and black cards as in a standard 52 card deck.
Solution: In a standard 52 card deck, half of the cards (26) are black and half are red. If you take 26 cards at random from the deck, x of them will be black and y of them will be red, and x+y=26. As there are 26 of each color in the deck, then x+?=26 for the black cards in the deck and ?+y=26 for the red cards in the deck. As x+y=26 in the first randomly selected 26 cards, then the value of black cards in the other half of the deck must equal y, and the value of red cards in the other half of the deck must equal x meaning that "there will always be as many red cards in the first half of the deck as there are black cards in the second half of the deck."

==16. Suppose that each daughter in your family has the same number of brothers as she has sisters, and each son in your family has twice as many sisters as he has brothers. How many sons and daughters are in the family?==

Answer:3 total, 2 sister and 1 brother
Solution: Since the daughters in the family each have as many brothers as sisters the amount of sisters, with x standing for the amount of brothers, is x+1. As each brother has twice as many sisters as brothers, the amount of sisters must equal 2(x-1) or 2x-2. To find the number of brother: x+1=2x+1, 1=x-2, 3=x, which means that their are 3 brothers and 4 sisters (x+1= the number of sisters and x=3). This makes sense because a sister would have an equal amount of brothers to sisters, 3 sisters and 3 brothers, if there were 4 sisters and 3 brothers total, and each brother would have 4 sisters and 3 brothers, which is twice the amount of brothers to sisters.

==17~21==
==Audrey Chen==

==17.The zero point on a bathroom scale is set incorrectly, but otherwise the scale is accurate. It shows 60 kg when Dan stands on the scale, 50 kg when Sarah stands on the scale, but 105 kg when Dan and Sarah both stand on the scale. Does the scale read too high or too low? Explain. ==

''The scale read too low, since Dan is shown as 60kg and Sarah is 50kg, suppose 60+50=110, 105-110=-5, so that means the scale is smaller than 0 in the beginning''

==18. Alice takes one-third of the pennies from a large jar. Then Bret takes one-third of the remaining pennies from the jar. Finally, Carla takes one-third of the remaining pennies from the jar, leaving 40 pennies in the jar. How many pennies were in the jar at the start? ==

''If the total pennies is "x", Alice take 1/3x, so it has 2/3x left after Alice took it, than Bret take 1/3 out, after Alice took it, which is 2/3x*1/3= 2/9x, so in the beginning they have x, after Alice took it, it has 2/3x left, and Bret took 2/9x, so after Bret took it, it becomes 2/3x-2/9x= 4/9x-2/9x=2/9x left in the jar. Than Carla take 1/3 of the rest, so she took 1/3 of rest which is 2/9x*1/3=3/27x, so Alice took 1/3x, Bret tool 2/9x, Carla took 3/27x, three of them totaly took 1/3x+2/9x+3/27x=18/27x, so there still has x-18/27x= 9/27x= 1/3 left, 1/3x=40pennies, so x=120 pennies, so it was having 120 pennies in the jar.

==19. One morning each member of Angela's family drank an eight-ounce cup of coffee and milk, with the (nonzero) amounts of coffee and milk varying from cup to cup. Angela drank a quarter of the total amount of milk and a sixth of the total amount of coffee. What is the least number of people in the family? ==

''If we let total milk is x, total coffee is y. Than 1/4x+1/6y=8, and because every cup is 8ounce, x+y is multiple by 8. So make it easier, we use 1/4x+1/6y=8 * 12 to both sides. than we will got 3x+2y=96, now we have 3x+2y=96 and x+y is multiple of 8, and the number that multiple by 8 is 8, 16, 24, 32... so 2x+2y= 16, 32, 48, 64, 80, 96, since 3x+2y=96, it can't be more than 96. It will only have 6 possible number, so if you take 3x+2y=96 substracting 2x+2y=16, 32, 48, 64, 80, 96 you can get 6 possible x, which are 80, 64, 48, 32, 16, and 0. Than put the number into 3x+2y=96, if you put 80 in, will get 20, which is bigger than 8, and also 64, 48. If we use 32, it will equal to 8, but that means we have 0 coffee, but coffee can't be 0, so there's only 16 and 0 left. Since Angela had 1/4 of total amount of milk, milk can't be 0. So we got 16ounce than 16*(1/4)=4, so that means she had 8-4=4 's coffee. So 4=1/6 coffee, than the total amount of coffee would be 4*6=24. than x=16 and y=24, 16+24=40 40/8ounce=5, so at least have 5 cups of drinks, so that means at least they have 5 members in Angela's family.''

==20.Of two clocks next to each other, one runs 5 min per hour fast and the other runs 5 min per hour slow. At midnight the clocks show the same time. At what time are they are one hour apart? ==

''Since one clock runs 5 min faster per hour, the other is 5 min slower, after clock runs an hour, two clocks will have 10 min different from each other. 60 min an hour. 60/10=6, so after 6 hours two clocks will having one hour apart, and that would be 6AM.''

==21.Sven placed exactly in the middle among all runners in a race. Dan was slower than Sven, in 10th place, and Lars was in 16th place. How many runners were in the race? ==

''There were 17 runners. Since lars was in 16th place, the runners at least have to be 16, than if Sven is placed exactly in the middle, it means it would have even number of runners. Because Dan is slower and he was at 10 place that tells us Seven has to be before 10th, and if there has 19 runners, Sven and Dan would be at the same place, so it should be 17 runners, than Sven would be at exactly in the middle which at 9th place.''

==22-25==

Roland Will

22. During a vacation, it rained on 13 days, but when it rained in the morning, the afternoon was sunny, and every rainy afternoon was preceded by a sunny morning. There were 11 sunny mornings and 12 sunny afternoons. How long was the vacation?

Answer: 18 days of vacation.

Solution: 13 of the days of vacation were half sunny and half rainy. As there were 23 sunny mornings and afternoons (11 sunny mornings+12 sunny afternoons = 23 sunny mornings and afternoons), 13 of those sunny afternoons or mornings were on half rainy days. This means there are 10 sunny half-days left over, which equal 5 sunny full days. The 5 sunny full days plus the 13 half sunny/rainy days equal 18 total days of vacation.

23. Suppose you overhear the following conversation: Paul: How old are your three children? Paula: The product of their ages is 36 and the sum of their ages is the same as today's date. Paul: That is not enough information. Paula: The oldest child also has red hair. If you were Paul could you determine the ages of Paula's children? Explain.

Answer: If I were Paul this might be possible, but since we don’t know the date that Paula said this, it is not possible for us to find out.

Solution: There are many different combinations of three numbers that can be multiplied and will produce 36. As we do not know the date that Paula said this, the only thing we can be sure of is that the sum of the ages is less than 31 because no month has more than 31 days. Unfortunately, only one set of ages (ages 1 year old, 1 year old and 36 years old) has a sum greater than 31, which leaves many possible combinations open as possible. For today’s date, the 13th, ages of 2, 2, and 9 would produce 36 and have a sum of 13, but, again, it is uncertain. If it were the first of the month, there would be no possible combinations that would produce 36 and sum 1.

24. Two candles of equal length were lit at the same time. One candle took 6 hr to burn out and the other candle took 3 hr to burn out. After how much time was one candle exactly twice as long as the other candle?

Answer: 2 hours.

Solution: The faster burning candle took half the time to burn as the slower burning candle (3 hours/ 6 hours = 1/2), meaning it burned twice as fast. This means that after 2/3 of the total burning time for the faster burning candle it will be 1/3 of its original height and at the slower burning candle will be at 2/3 of its original height and 1/3 is half of 2/3. Since the faster burning candle took 3 hours to burn, 2/3 of its total burning time is 2 hours.

==25. Two candles of length L and L + 1 were lit at 6:00 and 4:30, respectively. At 8:30 they had the same length. The longer candle died at 10:30 and the shorter candle died at 10:00. Find L.==

Answer: L=2.

Solution: The shorter candle lasted for 4 hours and the longer candle lasted for 6 hours. As 6 hours – 4 hours = 2 hours and 2 hours / 4 hours = 1/2, the longer candle lasted 50% longer and was, therefore, 50% longer in length. This means that the +1 in L+1 on the longer candle was 1/2 of L. 1/2L=1, so L=2*1, L=2.

Course:MATH110/Archive/2010-2011/003/Groups/Group 18

2010-10-29T07:58:23Z

RolandWill: /* 23. Suppose you overhear the following conversation: Paul: How old are your three children? Paula: The product of their ages is 36 and the sum of their ages is the same as today's date. Paul: That is not enough information. Paula: The oldest child

{{Infobox MATH110 Groups
| group number = 18
| member 1 = [[User:ChouJuChen|Audrey Chen]]
| member 2 = [[User:SifatHasan|Sifat Hasan]]
| member 3 = [[User:CaitlinLastiwkaFarquharson|Caitlin Lastiwka-Farquharson]]
| member 4 = [[User:VictoriaWall|Victoria Wall]]
| member 5 = [[User:RolandWill|Roland Will]]
| member 6 =
}}

==Homework due October 20th, 2010==

I created a page for our homework due tomorrow: [http://wiki.ubc.ca/Course:MATH110/003/Groups/Group_18/Homework_October_20th,_2010 http://wiki.ubc.ca/Course:MATH110/003/Groups/Group 18/Homework October 20th, 2010]

-Roland

I've moved the page, it was missing the ''Course:'' part which means it was created directly inside the wiki and not as a subpage of your group page, which is something the wiki admins don't like that much. By the way, you're allowed to use spaces in the name of your pages.

-- [[User:DavidKohler|DavidKohler]] 06:28, 20 October 2010 (UTC)

==1-5==
==Victoria Wall ==
==1.A bus traveled from the terminal to the airport at an average speed of 30 mi/hr and the trip took an hour and 20 min. The bus then traveled from the airport back to the terminal and again averaged 30 mi/hr. However, the return trip required 80 min. Explain.==

' 'Lets call the terminal T and the airport A. If the bus travelled from T to A at 30mi/hr and it took them one hour and 20 mins to get from T to A at this speed, and there are 60 minutes in one hour, it took the bus 60min + 20min to get to A which is a total of 80min. The bus took 80 min to get from T to A. To get from A to T at the same speed (30mi/hr) it took the bus 80min. 80min = 80 min. This means going from A to T or vis versa at 30 mi/hr it will take the bus 80min.

==2.A lady did not have her driver's license with her when she failed to stop at a stop sign and then went three blocks down a one-way street the wrong way. A policeman saw her, but he did not stop her. Explain. ==

' 'The lady was walking. It never says she was driving.

==3.One of three boxes contains apples, another box contains oranges, and another box contains a mixture of apples and oranges. The boxes are labeled APPLES, ORANGES and APPLES AND ORANGES, but each label is incorrect. Can you select one fruit from only one box and determine the correct labels? Explain. ==

' 'if you selecet from the box APPLES AND ORANGES then you will be able to see the labels if they are correct or not.

==4.I am the brother of the blind fiddler, but brothers I have none. How can this be? ==

' 'Since it says that he is the brother of the blind fiddler it does not mean that the fiddle is male, since he has no brothers than the fiddler must be a female.

==5.Two quarters rest next to each other on a table. One coin is held fixed while the second coin is rolled around the edge of the first coin with no slipping. When the moving coin returns to its original position, how many times has it revolved? ==

' 'This is because the moving quarters revolves two full revolutions

==6-10==
== Caitlin Lastiwka- Farquharson ==

==6. Three kinds of apples are all mixed up in a basket. How many apples must you draw without (without looking) from the basket to be sure of getting at least two of a kind? ==

' ' To be sure you are getting at least two of a kind, you must select all of the other types of apples, plus two more. Meaning that only once you have selected all of the other apples can you be sure that you will select two of the kind you desire. It can be written like this: x,a x2, b and x3, c, with x representing the quantity of apples. This can be calculated by x2 + x3 +2. X2 representing one of the types of apples, x3 representing the other type and 2 representing 2 of the kind of apples you are trying to select. This is the only way to be sure you are getting at least two of a kind. ' '

==7. Suppose you have 40 blue socks and 40 brown socks in a drawer. How many socks must you take from the drawer (without looking) to be sure of getting (i) a pair of the same colour, and (ii) a pair with different colors. ==

' 'You must take three socks from the drawer to ensure you have a pair that match. This is because if you only select two, one could be brown and one could be blue. Selecting three, ensures that at least two of them will be the same colour. As for part two, you would need to select 41 socks to ensure you had a pair of different coloured socks because if you select 40 or less you could get all the same colour, but selecting 41 ensures you will have at least one pair of mixed colour. ' '

==8. Rueben says "Two days ago I was 20 years old. Later next year I will be 23 years old." Explain how this is possible. ==

' 'It is possible if your birthday is on the 31st of December and today is the 1st of January. This is because on the 30th of December (two days ago) you we’re 20 years old and now you are 21, later this year you will turn 22 on the 31st of December, and therefore 23 the next year.' '

==9. A rope ladder hanging over the side of a boat has rungs one foot apart. Ten rungs are showing. If the tide rises five feet, how many rungs will be showing? ==

' ' 5 rungs will be showing, because if there are 10 showing now, and they are each a foot apart, then for 5 more rungs to be showing there would need to be an increase in the level of water by 5 feet. ' '

==10.Suppose one-half of all people are chocolate eaters and one-half of all people are women. (i) Does it follow that one-fourth of all people are women chocolate eaters? (ii) Does it follow that one-half of all men are chocolate eaters? Explain. ==

' ' No, it does not follow that one-fourth of all people are women chocolate eaters and it does not follow that half of all men are chocolate eaters because are completely independent scenarios. Meaning that the the amount of women there are does not influence the amount of men that will eat chocolate. For example, If 50% of people are women and 50% of the entire population including men and women eat chocolate (arrived at by using the same logic that if 1/4 of women eat chocolate and 1/4 of men eat chocolate), that entire 50% could be comprised of women, meaning that no men eat chocolate disproving the statement.

==11-14==
==Sifat Hasan==

==11 11. A woman, her older brother, her son, and her daughter are chess players. The worst player’s twin, who is one of the four players, and the best player are of opposite sex. The worst player and the best player have the same age. If this is possible, who is the worst player?==

The four players (according to age, from oldest to youngest) are: woman's older brother, woman, and the son and the daughter (of the same age). Assuming that the children are of the same age (i.e. twins), the worst player is one of them, since they are the only ones who can have a twin. Assuming that the worst player is the daughter, her brother the son, is of the opposite sex as the woman, therefore the woman is the worst player. However, since the worst and the best player are of the same age, this is not possible, because the twins are of the opposite sex and they are of different genders.

==12 A Manhattan fellow had a girlfriend in the Bronx and a girlfriend in Brooklyn. He decided which girlfriend to visit by arriving randomly at the train station and taking the first of the Bronx or Brooklyn trains that arrived. The trains to Brooklyn and the Bronx each arrived regularly every 10 minutes. Not long after he began his scheme the man's Bronx girlfriend left him because he rarely visited. Give a (logical) explanation==

Assuming that the Bronx and the Brooklyn train arrive one after the other every 10 minutes, the only logical explanation would be that the man in Manhattan coincidentally went to the station 10 minutes or less before a train to Brooklyn arrived, most of the time.

==13 If a clock takes 5 seconds to strike 5:00 (with 5 equally spaced chimes), how long does it take to strike 10:00 (with 10 equally spaced chimes)?==

If it takes 5 seconds to strike 5, there will be 4 little halts in the middle. Therefore it takes 5 chimes 4 (5/4) = 1.25 second halts to finish. For 10 chimes, there are 9 halts so, it takes 9x 1.25 = 11.25 seconds for 10 halts.

==14 One day in the maternity ward, the name tags for four girl babies became mixed up. (i) In how many different ways could two of the babies be tagged correctly and two of the babies be tagged incorrectly? (ii) In how many different ways could three of the babies be tagged correctly and one baby be tagged incorrectly?==

(i)and (ii) If we take the babies names as A,B,C and D. There are 6 different combinations of the mix up, that two babies' names can be correct and 2 can be wrong. Assuming the name tags for the babies A,B,C and D are in respective order, they are ABDC, ADCB, ACBD, DBCA, CBAD and BACD. All other combinations for example BCAD will have one correct and 3 incorrect, or all four of them correct, because if 3 are correct, the fourth one has to be correct.

==15-16==
==Roland Will==

==15. Alex says to you, “I'll bet you any amount of money that if I shuffle this deck of cards, there will always be as many red cards in the first half of the deck as there are black cards in the second half of the deck.” Should you accept his bet?==

Answer: No, you shouldn't assuming the deck has equal amounts of red and black cards as in a standard 52 card deck.
Solution: In a standard 52 card deck, half of the cards (26) are black and half are red. If you take 26 cards at random from the deck, x of them will be black and y of them will be red, and x+y=26. As there are 26 of each color in the deck, then x+?=26 for the black cards in the deck and ?+y=26 for the red cards in the deck. As x+y=26 in the first randomly selected 26 cards, then the value of black cards in the other half of the deck must equal y, and the value of red cards in the other half of the deck must equal x meaning that "there will always be as many red cards in the first half of the deck as there are black cards in the second half of the deck."

==16. Suppose that each daughter in your family has the same number of brothers as she has sisters, and each son in your family has twice as many sisters as he has brothers. How many sons and daughters are in the family?==

Answer:3 total, 2 sister and 1 brother
Solution: Since the daughters in the family each have as many brothers as sisters the amount of sisters, with x standing for the amount of brothers, is x+1. As each brother has twice as many sisters as brothers, the amount of sisters must equal 2(x-1) or 2x-2. To find the number of brother: x+1=2x+1, 1=x-2, 3=x, which means that their are 3 brothers and 4 sisters (x+1= the number of sisters and x=3). This makes sense because a sister would have an equal amount of brothers to sisters, 3 sisters and 3 brothers, if there were 4 sisters and 3 brothers total, and each brother would have 4 sisters and 3 brothers, which is twice the amount of brothers to sisters.

==17~21==
==Audrey Chen==

==17.The zero point on a bathroom scale is set incorrectly, but otherwise the scale is accurate. It shows 60 kg when Dan stands on the scale, 50 kg when Sarah stands on the scale, but 105 kg when Dan and Sarah both stand on the scale. Does the scale read too high or too low? Explain. ==

''The scale read too low, since Dan is shown as 60kg and Sarah is 50kg, suppose 60+50=110, 105-110=-5, so that means the scale is smaller than 0 in the beginning''

==18. Alice takes one-third of the pennies from a large jar. Then Bret takes one-third of the remaining pennies from the jar. Finally, Carla takes one-third of the remaining pennies from the jar, leaving 40 pennies in the jar. How many pennies were in the jar at the start? ==

''If the total pennies is "x", Alice take 1/3x, so it has 2/3x left after Alice took it, than Bret take 1/3 out, after Alice took it, which is 2/3x*1/3= 2/9x, so in the beginning they have x, after Alice took it, it has 2/3x left, and Bret took 2/9x, so after Bret took it, it becomes 2/3x-2/9x= 4/9x-2/9x=2/9x left in the jar. Than Carla take 1/3 of the rest, so she took 1/3 of rest which is 2/9x*1/3=3/27x, so Alice took 1/3x, Bret tool 2/9x, Carla took 3/27x, three of them totaly took 1/3x+2/9x+3/27x=18/27x, so there still has x-18/27x= 9/27x= 1/3 left, 1/3x=40pennies, so x=120 pennies, so it was having 120 pennies in the jar.

==19. One morning each member of Angela's family drank an eight-ounce cup of coffee and milk, with the (nonzero) amounts of coffee and milk varying from cup to cup. Angela drank a quarter of the total amount of milk and a sixth of the total amount of coffee. What is the least number of people in the family? ==

''If we let total milk is x, total coffee is y. Than 1/4x+1/6y=8, and because every cup is 8ounce, x+y is multiple by 8. So make it easier, we use 1/4x+1/6y=8 * 12 to both sides. than we will got 3x+2y=96, now we have 3x+2y=96 and x+y is multiple of 8, and the number that multiple by 8 is 8, 16, 24, 32... so 2x+2y= 16, 32, 48, 64, 80, 96, since 3x+2y=96, it can't be more than 96. It will only have 6 possible number, so if you take 3x+2y=96 substracting 2x+2y=16, 32, 48, 64, 80, 96 you can get 6 possible x, which are 80, 64, 48, 32, 16, and 0. Than put the number into 3x+2y=96, if you put 80 in, will get 20, which is bigger than 8, and also 64, 48. If we use 32, it will equal to 8, but that means we have 0 coffee, but coffee can't be 0, so there's only 16 and 0 left. Since Angela had 1/4 of total amount of milk, milk can't be 0. So we got 16ounce than 16*(1/4)=4, so that means she had 8-4=4 's coffee. So 4=1/6 coffee, than the total amount of coffee would be 4*6=24. than x=16 and y=24, 16+24=40 40/8ounce=5, so at least have 5 cups of drinks, so that means at least they have 5 members in Angela's family.''

==20.Of two clocks next to each other, one runs 5 min per hour fast and the other runs 5 min per hour slow. At midnight the clocks show the same time. At what time are they are one hour apart? ==

''Since one clock runs 5 min faster per hour, the other is 5 min slower, after clock runs an hour, two clocks will have 10 min different from each other. 60 min an hour. 60/10=6, so after 6 hours two clocks will having one hour apart, and that would be 6AM.''

==21.Sven placed exactly in the middle among all runners in a race. Dan was slower than Sven, in 10th place, and Lars was in 16th place. How many runners were in the race? ==

''There were 17 runners. Since lars was in 16th place, the runners at least have to be 16, than if Sven is placed exactly in the middle, it means it would have even number of runners. Because Dan is slower and he was at 10 place that tells us Seven has to be before 10th, and if there has 19 runners, Sven and Dan would be at the same place, so it should be 17 runners, than Sven would be at exactly in the middle which at 9th place.''

==22-25==

Roland Will

22. During a vacation, it rained on 13 days, but when it rained in the morning, the afternoon was sunny, and every rainy afternoon was preceded by a sunny morning. There were 11 sunny mornings and 12 sunny afternoons. How long was the vacation?

Answer: 18 days of vacation.

Solution: 13 of the days of vacation were half sunny and half rainy. As there were 23 sunny mornings and afternoons (11 sunny mornings+12 sunny afternoons = 23 sunny mornings and afternoons), 13 of those sunny afternoons or mornings were on half rainy days. This means there are 10 sunny half-days left over, which equal 5 sunny full days. The 5 sunny full days plus the 13 half sunny/rainy days equal 18 total days of vacation.

23. Suppose you overhear the following conversation: Paul: How old are your three children? Paula: The product of their ages is 36 and the sum of their ages is the same as today's date. Paul: That is not enough information. Paula: The oldest child also has red hair. If you were Paul could you determine the ages of Paula's children? Explain.

Answer: If I were Paul this might be possible, but since we don’t know the date that Paula said this, it is not possible for us to find out.

Solution: There are many different combinations of three numbers that can be multiplied and will produce 36. As we do not know the date that Paula said this, the only thing we can be sure of is that the sum of the ages is less than 31 because no month has more than 31 days. Unfortunately, only one set of ages (ages 1 year old, 1 year old and 36 years old) has a sum greater than 31, which leaves many possible combinations open as possible. For today’s date, the 13th, ages of 2, 2, and 9 would produce 36 and have a sum of 13, but, again, it is uncertain. If it were the first of the month, there would be no possible combinations that would produce 36 and sum 1.

==24. Two candles of equal length were lit at the same time. One candle took 6 hr to burn out and the other candle took 3 hr to burn out. After how much time was one candle exactly twice as long as the other candle?==

Answer: 2 hours.

Solution: The faster burning candle took half the time to burn as the slower burning candle (3 hours/ 6 hours = 1/2), meaning it burned twice as fast. This means that after 2/3 of the total burning time for the faster burning candle it will be 1/3 of its original height and at the slower burning candle will be at 2/3 of its original height and 1/3 is half of 2/3. Since the faster burning candle took 3 hours to burn, 2/3 of its total burning time is 2 hours.

==25. Two candles of length L and L + 1 were lit at 6:00 and 4:30, respectively. At 8:30 they had the same length. The longer candle died at 10:30 and the shorter candle died at 10:00. Find L.==

Answer: L=2.

Solution: The shorter candle lasted for 4 hours and the longer candle lasted for 6 hours. As 6 hours – 4 hours = 2 hours and 2 hours / 4 hours = 1/2, the longer candle lasted 50% longer and was, therefore, 50% longer in length. This means that the +1 in L+1 on the longer candle was 1/2 of L. 1/2L=1, so L=2*1, L=2.

Course:MATH110/Archive/2010-2011/003/Groups/Group 18

2010-10-29T07:57:51Z

RolandWill: /* Roland Will */

{{Infobox MATH110 Groups
| group number = 18
| member 1 = [[User:ChouJuChen|Audrey Chen]]
| member 2 = [[User:SifatHasan|Sifat Hasan]]
| member 3 = [[User:CaitlinLastiwkaFarquharson|Caitlin Lastiwka-Farquharson]]
| member 4 = [[User:VictoriaWall|Victoria Wall]]
| member 5 = [[User:RolandWill|Roland Will]]
| member 6 =
}}

==Homework due October 20th, 2010==

I created a page for our homework due tomorrow: [http://wiki.ubc.ca/Course:MATH110/003/Groups/Group_18/Homework_October_20th,_2010 http://wiki.ubc.ca/Course:MATH110/003/Groups/Group 18/Homework October 20th, 2010]

-Roland

I've moved the page, it was missing the ''Course:'' part which means it was created directly inside the wiki and not as a subpage of your group page, which is something the wiki admins don't like that much. By the way, you're allowed to use spaces in the name of your pages.

-- [[User:DavidKohler|DavidKohler]] 06:28, 20 October 2010 (UTC)

==1-5==
==Victoria Wall ==
==1.A bus traveled from the terminal to the airport at an average speed of 30 mi/hr and the trip took an hour and 20 min. The bus then traveled from the airport back to the terminal and again averaged 30 mi/hr. However, the return trip required 80 min. Explain.==

' 'Lets call the terminal T and the airport A. If the bus travelled from T to A at 30mi/hr and it took them one hour and 20 mins to get from T to A at this speed, and there are 60 minutes in one hour, it took the bus 60min + 20min to get to A which is a total of 80min. The bus took 80 min to get from T to A. To get from A to T at the same speed (30mi/hr) it took the bus 80min. 80min = 80 min. This means going from A to T or vis versa at 30 mi/hr it will take the bus 80min.

==2.A lady did not have her driver's license with her when she failed to stop at a stop sign and then went three blocks down a one-way street the wrong way. A policeman saw her, but he did not stop her. Explain. ==

' 'The lady was walking. It never says she was driving.

==3.One of three boxes contains apples, another box contains oranges, and another box contains a mixture of apples and oranges. The boxes are labeled APPLES, ORANGES and APPLES AND ORANGES, but each label is incorrect. Can you select one fruit from only one box and determine the correct labels? Explain. ==

' 'if you selecet from the box APPLES AND ORANGES then you will be able to see the labels if they are correct or not.

==4.I am the brother of the blind fiddler, but brothers I have none. How can this be? ==

' 'Since it says that he is the brother of the blind fiddler it does not mean that the fiddle is male, since he has no brothers than the fiddler must be a female.

==5.Two quarters rest next to each other on a table. One coin is held fixed while the second coin is rolled around the edge of the first coin with no slipping. When the moving coin returns to its original position, how many times has it revolved? ==

' 'This is because the moving quarters revolves two full revolutions

==6-10==
== Caitlin Lastiwka- Farquharson ==

==6. Three kinds of apples are all mixed up in a basket. How many apples must you draw without (without looking) from the basket to be sure of getting at least two of a kind? ==

' ' To be sure you are getting at least two of a kind, you must select all of the other types of apples, plus two more. Meaning that only once you have selected all of the other apples can you be sure that you will select two of the kind you desire. It can be written like this: x,a x2, b and x3, c, with x representing the quantity of apples. This can be calculated by x2 + x3 +2. X2 representing one of the types of apples, x3 representing the other type and 2 representing 2 of the kind of apples you are trying to select. This is the only way to be sure you are getting at least two of a kind. ' '

==7. Suppose you have 40 blue socks and 40 brown socks in a drawer. How many socks must you take from the drawer (without looking) to be sure of getting (i) a pair of the same colour, and (ii) a pair with different colors. ==

' 'You must take three socks from the drawer to ensure you have a pair that match. This is because if you only select two, one could be brown and one could be blue. Selecting three, ensures that at least two of them will be the same colour. As for part two, you would need to select 41 socks to ensure you had a pair of different coloured socks because if you select 40 or less you could get all the same colour, but selecting 41 ensures you will have at least one pair of mixed colour. ' '

==8. Rueben says "Two days ago I was 20 years old. Later next year I will be 23 years old." Explain how this is possible. ==

' 'It is possible if your birthday is on the 31st of December and today is the 1st of January. This is because on the 30th of December (two days ago) you we’re 20 years old and now you are 21, later this year you will turn 22 on the 31st of December, and therefore 23 the next year.' '

==9. A rope ladder hanging over the side of a boat has rungs one foot apart. Ten rungs are showing. If the tide rises five feet, how many rungs will be showing? ==

' ' 5 rungs will be showing, because if there are 10 showing now, and they are each a foot apart, then for 5 more rungs to be showing there would need to be an increase in the level of water by 5 feet. ' '

==10.Suppose one-half of all people are chocolate eaters and one-half of all people are women. (i) Does it follow that one-fourth of all people are women chocolate eaters? (ii) Does it follow that one-half of all men are chocolate eaters? Explain. ==

' ' No, it does not follow that one-fourth of all people are women chocolate eaters and it does not follow that half of all men are chocolate eaters because are completely independent scenarios. Meaning that the the amount of women there are does not influence the amount of men that will eat chocolate. For example, If 50% of people are women and 50% of the entire population including men and women eat chocolate (arrived at by using the same logic that if 1/4 of women eat chocolate and 1/4 of men eat chocolate), that entire 50% could be comprised of women, meaning that no men eat chocolate disproving the statement.

==11-14==
==Sifat Hasan==

==11 11. A woman, her older brother, her son, and her daughter are chess players. The worst player’s twin, who is one of the four players, and the best player are of opposite sex. The worst player and the best player have the same age. If this is possible, who is the worst player?==

The four players (according to age, from oldest to youngest) are: woman's older brother, woman, and the son and the daughter (of the same age). Assuming that the children are of the same age (i.e. twins), the worst player is one of them, since they are the only ones who can have a twin. Assuming that the worst player is the daughter, her brother the son, is of the opposite sex as the woman, therefore the woman is the worst player. However, since the worst and the best player are of the same age, this is not possible, because the twins are of the opposite sex and they are of different genders.

==12 A Manhattan fellow had a girlfriend in the Bronx and a girlfriend in Brooklyn. He decided which girlfriend to visit by arriving randomly at the train station and taking the first of the Bronx or Brooklyn trains that arrived. The trains to Brooklyn and the Bronx each arrived regularly every 10 minutes. Not long after he began his scheme the man's Bronx girlfriend left him because he rarely visited. Give a (logical) explanation==

Assuming that the Bronx and the Brooklyn train arrive one after the other every 10 minutes, the only logical explanation would be that the man in Manhattan coincidentally went to the station 10 minutes or less before a train to Brooklyn arrived, most of the time.

==13 If a clock takes 5 seconds to strike 5:00 (with 5 equally spaced chimes), how long does it take to strike 10:00 (with 10 equally spaced chimes)?==

If it takes 5 seconds to strike 5, there will be 4 little halts in the middle. Therefore it takes 5 chimes 4 (5/4) = 1.25 second halts to finish. For 10 chimes, there are 9 halts so, it takes 9x 1.25 = 11.25 seconds for 10 halts.

==14 One day in the maternity ward, the name tags for four girl babies became mixed up. (i) In how many different ways could two of the babies be tagged correctly and two of the babies be tagged incorrectly? (ii) In how many different ways could three of the babies be tagged correctly and one baby be tagged incorrectly?==

(i)and (ii) If we take the babies names as A,B,C and D. There are 6 different combinations of the mix up, that two babies' names can be correct and 2 can be wrong. Assuming the name tags for the babies A,B,C and D are in respective order, they are ABDC, ADCB, ACBD, DBCA, CBAD and BACD. All other combinations for example BCAD will have one correct and 3 incorrect, or all four of them correct, because if 3 are correct, the fourth one has to be correct.

==15-16==
==Roland Will==

==15. Alex says to you, “I'll bet you any amount of money that if I shuffle this deck of cards, there will always be as many red cards in the first half of the deck as there are black cards in the second half of the deck.” Should you accept his bet?==

Answer: No, you shouldn't assuming the deck has equal amounts of red and black cards as in a standard 52 card deck.
Solution: In a standard 52 card deck, half of the cards (26) are black and half are red. If you take 26 cards at random from the deck, x of them will be black and y of them will be red, and x+y=26. As there are 26 of each color in the deck, then x+?=26 for the black cards in the deck and ?+y=26 for the red cards in the deck. As x+y=26 in the first randomly selected 26 cards, then the value of black cards in the other half of the deck must equal y, and the value of red cards in the other half of the deck must equal x meaning that "there will always be as many red cards in the first half of the deck as there are black cards in the second half of the deck."

==16. Suppose that each daughter in your family has the same number of brothers as she has sisters, and each son in your family has twice as many sisters as he has brothers. How many sons and daughters are in the family?==

Answer:3 total, 2 sister and 1 brother
Solution: Since the daughters in the family each have as many brothers as sisters the amount of sisters, with x standing for the amount of brothers, is x+1. As each brother has twice as many sisters as brothers, the amount of sisters must equal 2(x-1) or 2x-2. To find the number of brother: x+1=2x+1, 1=x-2, 3=x, which means that their are 3 brothers and 4 sisters (x+1= the number of sisters and x=3). This makes sense because a sister would have an equal amount of brothers to sisters, 3 sisters and 3 brothers, if there were 4 sisters and 3 brothers total, and each brother would have 4 sisters and 3 brothers, which is twice the amount of brothers to sisters.

==17~21==
==Audrey Chen==

==17.The zero point on a bathroom scale is set incorrectly, but otherwise the scale is accurate. It shows 60 kg when Dan stands on the scale, 50 kg when Sarah stands on the scale, but 105 kg when Dan and Sarah both stand on the scale. Does the scale read too high or too low? Explain. ==

''The scale read too low, since Dan is shown as 60kg and Sarah is 50kg, suppose 60+50=110, 105-110=-5, so that means the scale is smaller than 0 in the beginning''

==18. Alice takes one-third of the pennies from a large jar. Then Bret takes one-third of the remaining pennies from the jar. Finally, Carla takes one-third of the remaining pennies from the jar, leaving 40 pennies in the jar. How many pennies were in the jar at the start? ==

''If the total pennies is "x", Alice take 1/3x, so it has 2/3x left after Alice took it, than Bret take 1/3 out, after Alice took it, which is 2/3x*1/3= 2/9x, so in the beginning they have x, after Alice took it, it has 2/3x left, and Bret took 2/9x, so after Bret took it, it becomes 2/3x-2/9x= 4/9x-2/9x=2/9x left in the jar. Than Carla take 1/3 of the rest, so she took 1/3 of rest which is 2/9x*1/3=3/27x, so Alice took 1/3x, Bret tool 2/9x, Carla took 3/27x, three of them totaly took 1/3x+2/9x+3/27x=18/27x, so there still has x-18/27x= 9/27x= 1/3 left, 1/3x=40pennies, so x=120 pennies, so it was having 120 pennies in the jar.

==19. One morning each member of Angela's family drank an eight-ounce cup of coffee and milk, with the (nonzero) amounts of coffee and milk varying from cup to cup. Angela drank a quarter of the total amount of milk and a sixth of the total amount of coffee. What is the least number of people in the family? ==

''If we let total milk is x, total coffee is y. Than 1/4x+1/6y=8, and because every cup is 8ounce, x+y is multiple by 8. So make it easier, we use 1/4x+1/6y=8 * 12 to both sides. than we will got 3x+2y=96, now we have 3x+2y=96 and x+y is multiple of 8, and the number that multiple by 8 is 8, 16, 24, 32... so 2x+2y= 16, 32, 48, 64, 80, 96, since 3x+2y=96, it can't be more than 96. It will only have 6 possible number, so if you take 3x+2y=96 substracting 2x+2y=16, 32, 48, 64, 80, 96 you can get 6 possible x, which are 80, 64, 48, 32, 16, and 0. Than put the number into 3x+2y=96, if you put 80 in, will get 20, which is bigger than 8, and also 64, 48. If we use 32, it will equal to 8, but that means we have 0 coffee, but coffee can't be 0, so there's only 16 and 0 left. Since Angela had 1/4 of total amount of milk, milk can't be 0. So we got 16ounce than 16*(1/4)=4, so that means she had 8-4=4 's coffee. So 4=1/6 coffee, than the total amount of coffee would be 4*6=24. than x=16 and y=24, 16+24=40 40/8ounce=5, so at least have 5 cups of drinks, so that means at least they have 5 members in Angela's family.''

==20.Of two clocks next to each other, one runs 5 min per hour fast and the other runs 5 min per hour slow. At midnight the clocks show the same time. At what time are they are one hour apart? ==

''Since one clock runs 5 min faster per hour, the other is 5 min slower, after clock runs an hour, two clocks will have 10 min different from each other. 60 min an hour. 60/10=6, so after 6 hours two clocks will having one hour apart, and that would be 6AM.''

==21.Sven placed exactly in the middle among all runners in a race. Dan was slower than Sven, in 10th place, and Lars was in 16th place. How many runners were in the race? ==

''There were 17 runners. Since lars was in 16th place, the runners at least have to be 16, than if Sven is placed exactly in the middle, it means it would have even number of runners. Because Dan is slower and he was at 10 place that tells us Seven has to be before 10th, and if there has 19 runners, Sven and Dan would be at the same place, so it should be 17 runners, than Sven would be at exactly in the middle which at 9th place.''

==22-25==

Roland Will

22. During a vacation, it rained on 13 days, but when it rained in the morning, the afternoon was sunny, and every rainy afternoon was preceded by a sunny morning. There were 11 sunny mornings and 12 sunny afternoons. How long was the vacation?

Answer: 18 days of vacation.

Solution: 13 of the days of vacation were half sunny and half rainy. As there were 23 sunny mornings and afternoons (11 sunny mornings+12 sunny afternoons = 23 sunny mornings and afternoons), 13 of those sunny afternoons or mornings were on half rainy days. This means there are 10 sunny half-days left over, which equal 5 sunny full days. The 5 sunny full days plus the 13 half sunny/rainy days equal 18 total days of vacation.

==23. Suppose you overhear the following conversation: Paul: How old are your three children? Paula: The product of their ages is 36 and the sum of their ages is the same as today's date. Paul: That is not enough information. Paula: The oldest child also has red hair. If you were Paul could you determine the ages of Paula's children? Explain.==

Answer: If I were Paul this might be possible, but since we don’t know the date that Paula said this, it is not possible for us to find out.

Solution: There are many different combinations of three numbers that can be multiplied and will produce 36. As we do not know the date that Paula said this, the only thing we can be sure of is that the sum of the ages is less than 31 because no month has more than 31 days. Unfortunately, only one set of ages (ages 1 year old, 1 year old and 36 years old) has a sum greater than 31, which leaves many possible combinations open as possible. For today’s date, the 13th, ages of 2, 2, and 9 would produce 36 and have a sum of 13, but, again, it is uncertain. If it were the first of the month, there would be no possible combinations that would produce 36 and sum 1.

==24. Two candles of equal length were lit at the same time. One candle took 6 hr to burn out and the other candle took 3 hr to burn out. After how much time was one candle exactly twice as long as the other candle?==

Answer: 2 hours.

Solution: The faster burning candle took half the time to burn as the slower burning candle (3 hours/ 6 hours = 1/2), meaning it burned twice as fast. This means that after 2/3 of the total burning time for the faster burning candle it will be 1/3 of its original height and at the slower burning candle will be at 2/3 of its original height and 1/3 is half of 2/3. Since the faster burning candle took 3 hours to burn, 2/3 of its total burning time is 2 hours.

==25. Two candles of length L and L + 1 were lit at 6:00 and 4:30, respectively. At 8:30 they had the same length. The longer candle died at 10:30 and the shorter candle died at 10:00. Find L.==

Answer: L=2.

Solution: The shorter candle lasted for 4 hours and the longer candle lasted for 6 hours. As 6 hours – 4 hours = 2 hours and 2 hours / 4 hours = 1/2, the longer candle lasted 50% longer and was, therefore, 50% longer in length. This means that the +1 in L+1 on the longer candle was 1/2 of L. 1/2L=1, so L=2*1, L=2.

Course:MATH110/Archive/2010-2011/003/Groups/Group 18

2010-10-29T07:57:35Z

RolandWill: /* 22. During a vacation, it rained on 13 days, but when it rained in the morning, the afternoon was sunny, and every rainy afternoon was preceded by a sunny morning. There were 11 sunny mornings and 12 sunny afternoons. How long was the vacation? */

{{Infobox MATH110 Groups
| group number = 18
| member 1 = [[User:ChouJuChen|Audrey Chen]]
| member 2 = [[User:SifatHasan|Sifat Hasan]]
| member 3 = [[User:CaitlinLastiwkaFarquharson|Caitlin Lastiwka-Farquharson]]
| member 4 = [[User:VictoriaWall|Victoria Wall]]
| member 5 = [[User:RolandWill|Roland Will]]
| member 6 =
}}

==Homework due October 20th, 2010==

I created a page for our homework due tomorrow: [http://wiki.ubc.ca/Course:MATH110/003/Groups/Group_18/Homework_October_20th,_2010 http://wiki.ubc.ca/Course:MATH110/003/Groups/Group 18/Homework October 20th, 2010]

-Roland

I've moved the page, it was missing the ''Course:'' part which means it was created directly inside the wiki and not as a subpage of your group page, which is something the wiki admins don't like that much. By the way, you're allowed to use spaces in the name of your pages.

-- [[User:DavidKohler|DavidKohler]] 06:28, 20 October 2010 (UTC)

==1-5==
==Victoria Wall ==
==1.A bus traveled from the terminal to the airport at an average speed of 30 mi/hr and the trip took an hour and 20 min. The bus then traveled from the airport back to the terminal and again averaged 30 mi/hr. However, the return trip required 80 min. Explain.==

' 'Lets call the terminal T and the airport A. If the bus travelled from T to A at 30mi/hr and it took them one hour and 20 mins to get from T to A at this speed, and there are 60 minutes in one hour, it took the bus 60min + 20min to get to A which is a total of 80min. The bus took 80 min to get from T to A. To get from A to T at the same speed (30mi/hr) it took the bus 80min. 80min = 80 min. This means going from A to T or vis versa at 30 mi/hr it will take the bus 80min.

==2.A lady did not have her driver's license with her when she failed to stop at a stop sign and then went three blocks down a one-way street the wrong way. A policeman saw her, but he did not stop her. Explain. ==

' 'The lady was walking. It never says she was driving.

==3.One of three boxes contains apples, another box contains oranges, and another box contains a mixture of apples and oranges. The boxes are labeled APPLES, ORANGES and APPLES AND ORANGES, but each label is incorrect. Can you select one fruit from only one box and determine the correct labels? Explain. ==

' 'if you selecet from the box APPLES AND ORANGES then you will be able to see the labels if they are correct or not.

==4.I am the brother of the blind fiddler, but brothers I have none. How can this be? ==

' 'Since it says that he is the brother of the blind fiddler it does not mean that the fiddle is male, since he has no brothers than the fiddler must be a female.

==5.Two quarters rest next to each other on a table. One coin is held fixed while the second coin is rolled around the edge of the first coin with no slipping. When the moving coin returns to its original position, how many times has it revolved? ==

' 'This is because the moving quarters revolves two full revolutions

==6-10==
== Caitlin Lastiwka- Farquharson ==

==6. Three kinds of apples are all mixed up in a basket. How many apples must you draw without (without looking) from the basket to be sure of getting at least two of a kind? ==

' ' To be sure you are getting at least two of a kind, you must select all of the other types of apples, plus two more. Meaning that only once you have selected all of the other apples can you be sure that you will select two of the kind you desire. It can be written like this: x,a x2, b and x3, c, with x representing the quantity of apples. This can be calculated by x2 + x3 +2. X2 representing one of the types of apples, x3 representing the other type and 2 representing 2 of the kind of apples you are trying to select. This is the only way to be sure you are getting at least two of a kind. ' '

==7. Suppose you have 40 blue socks and 40 brown socks in a drawer. How many socks must you take from the drawer (without looking) to be sure of getting (i) a pair of the same colour, and (ii) a pair with different colors. ==

' 'You must take three socks from the drawer to ensure you have a pair that match. This is because if you only select two, one could be brown and one could be blue. Selecting three, ensures that at least two of them will be the same colour. As for part two, you would need to select 41 socks to ensure you had a pair of different coloured socks because if you select 40 or less you could get all the same colour, but selecting 41 ensures you will have at least one pair of mixed colour. ' '

==8. Rueben says "Two days ago I was 20 years old. Later next year I will be 23 years old." Explain how this is possible. ==

' 'It is possible if your birthday is on the 31st of December and today is the 1st of January. This is because on the 30th of December (two days ago) you we’re 20 years old and now you are 21, later this year you will turn 22 on the 31st of December, and therefore 23 the next year.' '

==9. A rope ladder hanging over the side of a boat has rungs one foot apart. Ten rungs are showing. If the tide rises five feet, how many rungs will be showing? ==

' ' 5 rungs will be showing, because if there are 10 showing now, and they are each a foot apart, then for 5 more rungs to be showing there would need to be an increase in the level of water by 5 feet. ' '

==10.Suppose one-half of all people are chocolate eaters and one-half of all people are women. (i) Does it follow that one-fourth of all people are women chocolate eaters? (ii) Does it follow that one-half of all men are chocolate eaters? Explain. ==

' ' No, it does not follow that one-fourth of all people are women chocolate eaters and it does not follow that half of all men are chocolate eaters because are completely independent scenarios. Meaning that the the amount of women there are does not influence the amount of men that will eat chocolate. For example, If 50% of people are women and 50% of the entire population including men and women eat chocolate (arrived at by using the same logic that if 1/4 of women eat chocolate and 1/4 of men eat chocolate), that entire 50% could be comprised of women, meaning that no men eat chocolate disproving the statement.

==11-14==
==Sifat Hasan==

==11 11. A woman, her older brother, her son, and her daughter are chess players. The worst player’s twin, who is one of the four players, and the best player are of opposite sex. The worst player and the best player have the same age. If this is possible, who is the worst player?==

The four players (according to age, from oldest to youngest) are: woman's older brother, woman, and the son and the daughter (of the same age). Assuming that the children are of the same age (i.e. twins), the worst player is one of them, since they are the only ones who can have a twin. Assuming that the worst player is the daughter, her brother the son, is of the opposite sex as the woman, therefore the woman is the worst player. However, since the worst and the best player are of the same age, this is not possible, because the twins are of the opposite sex and they are of different genders.

==12 A Manhattan fellow had a girlfriend in the Bronx and a girlfriend in Brooklyn. He decided which girlfriend to visit by arriving randomly at the train station and taking the first of the Bronx or Brooklyn trains that arrived. The trains to Brooklyn and the Bronx each arrived regularly every 10 minutes. Not long after he began his scheme the man's Bronx girlfriend left him because he rarely visited. Give a (logical) explanation==

Assuming that the Bronx and the Brooklyn train arrive one after the other every 10 minutes, the only logical explanation would be that the man in Manhattan coincidentally went to the station 10 minutes or less before a train to Brooklyn arrived, most of the time.

==13 If a clock takes 5 seconds to strike 5:00 (with 5 equally spaced chimes), how long does it take to strike 10:00 (with 10 equally spaced chimes)?==

If it takes 5 seconds to strike 5, there will be 4 little halts in the middle. Therefore it takes 5 chimes 4 (5/4) = 1.25 second halts to finish. For 10 chimes, there are 9 halts so, it takes 9x 1.25 = 11.25 seconds for 10 halts.

==14 One day in the maternity ward, the name tags for four girl babies became mixed up. (i) In how many different ways could two of the babies be tagged correctly and two of the babies be tagged incorrectly? (ii) In how many different ways could three of the babies be tagged correctly and one baby be tagged incorrectly?==

(i)and (ii) If we take the babies names as A,B,C and D. There are 6 different combinations of the mix up, that two babies' names can be correct and 2 can be wrong. Assuming the name tags for the babies A,B,C and D are in respective order, they are ABDC, ADCB, ACBD, DBCA, CBAD and BACD. All other combinations for example BCAD will have one correct and 3 incorrect, or all four of them correct, because if 3 are correct, the fourth one has to be correct.

==15-16==
==Roland Will==

==15. Alex says to you, “I'll bet you any amount of money that if I shuffle this deck of cards, there will always be as many red cards in the first half of the deck as there are black cards in the second half of the deck.” Should you accept his bet?==

Answer: No, you shouldn't assuming the deck has equal amounts of red and black cards as in a standard 52 card deck.
Solution: In a standard 52 card deck, half of the cards (26) are black and half are red. If you take 26 cards at random from the deck, x of them will be black and y of them will be red, and x+y=26. As there are 26 of each color in the deck, then x+?=26 for the black cards in the deck and ?+y=26 for the red cards in the deck. As x+y=26 in the first randomly selected 26 cards, then the value of black cards in the other half of the deck must equal y, and the value of red cards in the other half of the deck must equal x meaning that "there will always be as many red cards in the first half of the deck as there are black cards in the second half of the deck."

==16. Suppose that each daughter in your family has the same number of brothers as she has sisters, and each son in your family has twice as many sisters as he has brothers. How many sons and daughters are in the family?==

Answer:3 total, 2 sister and 1 brother
Solution: Since the daughters in the family each have as many brothers as sisters the amount of sisters, with x standing for the amount of brothers, is x+1. As each brother has twice as many sisters as brothers, the amount of sisters must equal 2(x-1) or 2x-2. To find the number of brother: x+1=2x+1, 1=x-2, 3=x, which means that their are 3 brothers and 4 sisters (x+1= the number of sisters and x=3). This makes sense because a sister would have an equal amount of brothers to sisters, 3 sisters and 3 brothers, if there were 4 sisters and 3 brothers total, and each brother would have 4 sisters and 3 brothers, which is twice the amount of brothers to sisters.

==17~21==
==Audrey Chen==

==17.The zero point on a bathroom scale is set incorrectly, but otherwise the scale is accurate. It shows 60 kg when Dan stands on the scale, 50 kg when Sarah stands on the scale, but 105 kg when Dan and Sarah both stand on the scale. Does the scale read too high or too low? Explain. ==

''The scale read too low, since Dan is shown as 60kg and Sarah is 50kg, suppose 60+50=110, 105-110=-5, so that means the scale is smaller than 0 in the beginning''

==18. Alice takes one-third of the pennies from a large jar. Then Bret takes one-third of the remaining pennies from the jar. Finally, Carla takes one-third of the remaining pennies from the jar, leaving 40 pennies in the jar. How many pennies were in the jar at the start? ==

''If the total pennies is "x", Alice take 1/3x, so it has 2/3x left after Alice took it, than Bret take 1/3 out, after Alice took it, which is 2/3x*1/3= 2/9x, so in the beginning they have x, after Alice took it, it has 2/3x left, and Bret took 2/9x, so after Bret took it, it becomes 2/3x-2/9x= 4/9x-2/9x=2/9x left in the jar. Than Carla take 1/3 of the rest, so she took 1/3 of rest which is 2/9x*1/3=3/27x, so Alice took 1/3x, Bret tool 2/9x, Carla took 3/27x, three of them totaly took 1/3x+2/9x+3/27x=18/27x, so there still has x-18/27x= 9/27x= 1/3 left, 1/3x=40pennies, so x=120 pennies, so it was having 120 pennies in the jar.

==19. One morning each member of Angela's family drank an eight-ounce cup of coffee and milk, with the (nonzero) amounts of coffee and milk varying from cup to cup. Angela drank a quarter of the total amount of milk and a sixth of the total amount of coffee. What is the least number of people in the family? ==

''If we let total milk is x, total coffee is y. Than 1/4x+1/6y=8, and because every cup is 8ounce, x+y is multiple by 8. So make it easier, we use 1/4x+1/6y=8 * 12 to both sides. than we will got 3x+2y=96, now we have 3x+2y=96 and x+y is multiple of 8, and the number that multiple by 8 is 8, 16, 24, 32... so 2x+2y= 16, 32, 48, 64, 80, 96, since 3x+2y=96, it can't be more than 96. It will only have 6 possible number, so if you take 3x+2y=96 substracting 2x+2y=16, 32, 48, 64, 80, 96 you can get 6 possible x, which are 80, 64, 48, 32, 16, and 0. Than put the number into 3x+2y=96, if you put 80 in, will get 20, which is bigger than 8, and also 64, 48. If we use 32, it will equal to 8, but that means we have 0 coffee, but coffee can't be 0, so there's only 16 and 0 left. Since Angela had 1/4 of total amount of milk, milk can't be 0. So we got 16ounce than 16*(1/4)=4, so that means she had 8-4=4 's coffee. So 4=1/6 coffee, than the total amount of coffee would be 4*6=24. than x=16 and y=24, 16+24=40 40/8ounce=5, so at least have 5 cups of drinks, so that means at least they have 5 members in Angela's family.''

==20.Of two clocks next to each other, one runs 5 min per hour fast and the other runs 5 min per hour slow. At midnight the clocks show the same time. At what time are they are one hour apart? ==

''Since one clock runs 5 min faster per hour, the other is 5 min slower, after clock runs an hour, two clocks will have 10 min different from each other. 60 min an hour. 60/10=6, so after 6 hours two clocks will having one hour apart, and that would be 6AM.''

==21.Sven placed exactly in the middle among all runners in a race. Dan was slower than Sven, in 10th place, and Lars was in 16th place. How many runners were in the race? ==

''There were 17 runners. Since lars was in 16th place, the runners at least have to be 16, than if Sven is placed exactly in the middle, it means it would have even number of runners. Because Dan is slower and he was at 10 place that tells us Seven has to be before 10th, and if there has 19 runners, Sven and Dan would be at the same place, so it should be 17 runners, than Sven would be at exactly in the middle which at 9th place.''

==22-25==

==Roland Will==

22. During a vacation, it rained on 13 days, but when it rained in the morning, the afternoon was sunny, and every rainy afternoon was preceded by a sunny morning. There were 11 sunny mornings and 12 sunny afternoons. How long was the vacation?

Answer: 18 days of vacation.

Solution: 13 of the days of vacation were half sunny and half rainy. As there were 23 sunny mornings and afternoons (11 sunny mornings+12 sunny afternoons = 23 sunny mornings and afternoons), 13 of those sunny afternoons or mornings were on half rainy days. This means there are 10 sunny half-days left over, which equal 5 sunny full days. The 5 sunny full days plus the 13 half sunny/rainy days equal 18 total days of vacation.

==23. Suppose you overhear the following conversation: Paul: How old are your three children? Paula: The product of their ages is 36 and the sum of their ages is the same as today's date. Paul: That is not enough information. Paula: The oldest child also has red hair. If you were Paul could you determine the ages of Paula's children? Explain.==

Answer: If I were Paul this might be possible, but since we don’t know the date that Paula said this, it is not possible for us to find out.

Solution: There are many different combinations of three numbers that can be multiplied and will produce 36. As we do not know the date that Paula said this, the only thing we can be sure of is that the sum of the ages is less than 31 because no month has more than 31 days. Unfortunately, only one set of ages (ages 1 year old, 1 year old and 36 years old) has a sum greater than 31, which leaves many possible combinations open as possible. For today’s date, the 13th, ages of 2, 2, and 9 would produce 36 and have a sum of 13, but, again, it is uncertain. If it were the first of the month, there would be no possible combinations that would produce 36 and sum 1.

==24. Two candles of equal length were lit at the same time. One candle took 6 hr to burn out and the other candle took 3 hr to burn out. After how much time was one candle exactly twice as long as the other candle?==

Answer: 2 hours.

Solution: The faster burning candle took half the time to burn as the slower burning candle (3 hours/ 6 hours = 1/2), meaning it burned twice as fast. This means that after 2/3 of the total burning time for the faster burning candle it will be 1/3 of its original height and at the slower burning candle will be at 2/3 of its original height and 1/3 is half of 2/3. Since the faster burning candle took 3 hours to burn, 2/3 of its total burning time is 2 hours.

==25. Two candles of length L and L + 1 were lit at 6:00 and 4:30, respectively. At 8:30 they had the same length. The longer candle died at 10:30 and the shorter candle died at 10:00. Find L.==

Answer: L=2.

Solution: The shorter candle lasted for 4 hours and the longer candle lasted for 6 hours. As 6 hours – 4 hours = 2 hours and 2 hours / 4 hours = 1/2, the longer candle lasted 50% longer and was, therefore, 50% longer in length. This means that the +1 in L+1 on the longer candle was 1/2 of L. 1/2L=1, so L=2*1, L=2.

Course:MATH110/Archive/2010-2011/003/Groups/Group 18/Homework October 20th, 2010

2010-10-20T10:37:08Z

RolandWill: /* Roland Will's Answers */

==MATH110/003/Groups/Group18HomeworkOctober20th,2010==

==Victoria Wall==
Problem 1
Five persons named their pets after each other. From the following clues, can you decide which pet belongs to Suzan's mother?

Tosh owns a cat,
Bianca owns a frog that she loves,
Jaela owns a parrot which keeps calling her "darling, darling",
Jun owns a snake, don't mess with him,
Suzan is the name of the frog,
The cat is named Jun,
The name by which they call the turtle is the name of the woman whose pet is Tosh,
Finally, Suzan's mother's pet is Bianca.

tosh owns a cat names Jun
bianca owns a frog named suzan
Jun owns a snake named Bianca --- Jun is suzans mother

==Roland Will's work for problem 3==

Adam, Bobo, Charles, Ed, Hassan, Jason, Mathieu, Pascal and Sung have formed a baseball team. The following facts are true:

* Adam does not like the catcher,
-Adam is not the catcher

* Ed's sister is engaged to the second baseman,
-Ed isn't second baseman
-second baseman is not married

* The centre fielder is taller than the right fielder,
-The center fielder is the 1-8th tallest person
-The right fielder is the 2-9th tallest person

* Hassan and the third baseman live in the same building,
-Hassan isn't 3rd baseman

* Pascal and Charles each won $20 from the pitcher at a poker game,
-Pascal and Charles aren't the pitcher

* Ed and the outfielders play cards during their free time,
-Ed isn't an outfielder

* The pitcher's wife is the third baseman's sister,
-The pitcher is married

* All the battery and infield except Charles, Hassan and Adam are shorter than Sung,
-Charles, Hassan, and Adam are part of the battery or infield, so they are not outfielders
-Sung cannot be shorter than himself and he cannot be Charles, Hassan, or Adam, so Sung is not part of the battery or the infield
-Sung is the 4-8 tallest person
-Charles, Hassan and Adam are the 1-4 tallest people

* Pascal, Adam and the shortstop lost $100 each at the race track,
-Pascal and Adam are not the short stop

* The second baseman beat Pascal, Hassan, Bobo and the catcher at billiards,
-Pascal, Hassan, and Bobo are not the second baseman or the catcher

* Sung is in the process of getting a divorce,
-Sung is married

* The catcher and the third baseman each have two legitimate children,
-The catcher is married
-The third baseman is married
-Bobo, Ed, Jason, Mathieu and Pascal cannot be catcher or third base
-Pascal is first baseman
-Ed is Short Stop
-Hassan is pitcher
-Jason is second baseman
-Adam is third baseman
-Charles is catcher

* Ed, Pascal Jason, the right fielder and the centre fielder are bachelors, the others are all married
-Ed, Pascal, and Jason are not the right or center fielders
-Ed, Pascal and Jason can't be third baseman or pitcher
-Sung cannot be right or center fielder, therefore Sung is left fielder
-Adam, Bobo, Charles, Ed, Hassan, Jason, Mathieu, and Pascal are not left fielder
-Bobo is center fielder and Mathieu is right fielder so Adam, Charles, Hassan, and Sung are all married
-Adam, Charles, Hassan, and Sung cannot be second baseman

* The shortstop, the third baseman and Bobo all attended the fight,
-Bobo is not the short stop or the third baseman

* Mathieu is the shortest player of the team,
-Mathieu is not center fielder

Determine the positions of each player on the baseball team.

Note: On a baseball team there are three outfielders (right, centre and left), four infielders (first baseman, second baseman, third baseman and shortstop) and the battery (pitcher and catcher).

==Roland Will's Answers for problem 3==

Positions
*Catcher: Charles
*Pitcher: Hassan
*First Baseman: Pascal
*Second Baseman: Jason
*Short Stop: Ed
*Third Baseman: Adam
*Right Fielder: Mathieu
*Center Fielder: Bobo
*Left Fielder: Sung

Course:MATH110/Archive/2010-2011/003/Groups/Group 18/Homework October 20th, 2010

2010-10-20T10:36:51Z

RolandWill: /* Roland Will's work */

==MATH110/003/Groups/Group18HomeworkOctober20th,2010==

==Victoria Wall==
Problem 1
Five persons named their pets after each other. From the following clues, can you decide which pet belongs to Suzan's mother?

Tosh owns a cat,
Bianca owns a frog that she loves,
Jaela owns a parrot which keeps calling her "darling, darling",
Jun owns a snake, don't mess with him,
Suzan is the name of the frog,
The cat is named Jun,
The name by which they call the turtle is the name of the woman whose pet is Tosh,
Finally, Suzan's mother's pet is Bianca.

tosh owns a cat names Jun
bianca owns a frog named suzan
Jun owns a snake named Bianca --- Jun is suzans mother

==Roland Will's work for problem 3==

Adam, Bobo, Charles, Ed, Hassan, Jason, Mathieu, Pascal and Sung have formed a baseball team. The following facts are true:

* Adam does not like the catcher,
-Adam is not the catcher

* Ed's sister is engaged to the second baseman,
-Ed isn't second baseman
-second baseman is not married

* The centre fielder is taller than the right fielder,
-The center fielder is the 1-8th tallest person
-The right fielder is the 2-9th tallest person

* Hassan and the third baseman live in the same building,
-Hassan isn't 3rd baseman

* Pascal and Charles each won $20 from the pitcher at a poker game,
-Pascal and Charles aren't the pitcher

* Ed and the outfielders play cards during their free time,
-Ed isn't an outfielder

* The pitcher's wife is the third baseman's sister,
-The pitcher is married

* All the battery and infield except Charles, Hassan and Adam are shorter than Sung,
-Charles, Hassan, and Adam are part of the battery or infield, so they are not outfielders
-Sung cannot be shorter than himself and he cannot be Charles, Hassan, or Adam, so Sung is not part of the battery or the infield
-Sung is the 4-8 tallest person
-Charles, Hassan and Adam are the 1-4 tallest people

* Pascal, Adam and the shortstop lost $100 each at the race track,
-Pascal and Adam are not the short stop

* The second baseman beat Pascal, Hassan, Bobo and the catcher at billiards,
-Pascal, Hassan, and Bobo are not the second baseman or the catcher

* Sung is in the process of getting a divorce,
-Sung is married

* The catcher and the third baseman each have two legitimate children,
-The catcher is married
-The third baseman is married
-Bobo, Ed, Jason, Mathieu and Pascal cannot be catcher or third base
-Pascal is first baseman
-Ed is Short Stop
-Hassan is pitcher
-Jason is second baseman
-Adam is third baseman
-Charles is catcher

* Ed, Pascal Jason, the right fielder and the centre fielder are bachelors, the others are all married
-Ed, Pascal, and Jason are not the right or center fielders
-Ed, Pascal and Jason can't be third baseman or pitcher
-Sung cannot be right or center fielder, therefore Sung is left fielder
-Adam, Bobo, Charles, Ed, Hassan, Jason, Mathieu, and Pascal are not left fielder
-Bobo is center fielder and Mathieu is right fielder so Adam, Charles, Hassan, and Sung are all married
-Adam, Charles, Hassan, and Sung cannot be second baseman

* The shortstop, the third baseman and Bobo all attended the fight,
-Bobo is not the short stop or the third baseman

* Mathieu is the shortest player of the team,
-Mathieu is not center fielder

Determine the positions of each player on the baseball team.

Note: On a baseball team there are three outfielders (right, centre and left), four infielders (first baseman, second baseman, third baseman and shortstop) and the battery (pitcher and catcher).

==Roland Will's Answers==

Positions
*Catcher: Charles
*Pitcher: Hassan
*First Baseman: Pascal
*Second Baseman: Jason
*Short Stop: Ed
*Third Baseman: Adam
*Right Fielder: Mathieu
*Center Fielder: Bobo
*Left Fielder: Sung

Course:MATH110/Archive/2010-2011/003/Groups/Group 18/Homework October 20th, 2010

2010-10-20T10:30:33Z

RolandWill: /* Answers */

==MATH110/003/Groups/Group18HomeworkOctober20th,2010==

==Victoria Wall==
Problem 1
Five persons named their pets after each other. From the following clues, can you decide which pet belongs to Suzan's mother?

Tosh owns a cat,
Bianca owns a frog that she loves,
Jaela owns a parrot which keeps calling her "darling, darling",
Jun owns a snake, don't mess with him,
Suzan is the name of the frog,
The cat is named Jun,
The name by which they call the turtle is the name of the woman whose pet is Tosh,
Finally, Suzan's mother's pet is Bianca.

tosh owns a cat names Jun
bianca owns a frog named suzan
Jun owns a snake named Bianca --- Jun is suzans mother

==Roland Will's work==

Adam, Bobo, Charles, Ed, Hassan, Jason, Mathieu, Pascal and Sung have formed a baseball team. The following facts are true:

* Adam does not like the catcher,
-Adam is not the catcher

* Ed's sister is engaged to the second baseman,
-Ed isn't second baseman
-second baseman is not married

* The centre fielder is taller than the right fielder,
-The center fielder is the 1-8th tallest person
-The right fielder is the 2-9th tallest person

* Hassan and the third baseman live in the same building,
-Hassan isn't 3rd baseman

* Pascal and Charles each won $20 from the pitcher at a poker game,
-Pascal and Charles aren't the pitcher

* Ed and the outfielders play cards during their free time,
-Ed isn't an outfielder

* The pitcher's wife is the third baseman's sister,
-The pitcher is married

* All the battery and infield except Charles, Hassan and Adam are shorter than Sung,
-Charles, Hassan, and Adam are part of the battery or infield, so they are not outfielders
-Sung cannot be shorter than himself and he cannot be Charles, Hassan, or Adam, so Sung is not part of the battery or the infield
-Sung is the 4-8 tallest person
-Charles, Hassan and Adam are the 1-4 tallest people

* Pascal, Adam and the shortstop lost $100 each at the race track,
-Pascal and Adam are not the short stop

* The second baseman beat Pascal, Hassan, Bobo and the catcher at billiards,
-Pascal, Hassan, and Bobo are not the second baseman or the catcher

* Sung is in the process of getting a divorce,
-Sung is married

* The catcher and the third baseman each have two legitimate children,
-The catcher is married
-The third baseman is married
-Bobo, Ed, Jason, Mathieu and Pascal cannot be catcher or third base
-Pascal is first baseman
-Ed is Short Stop
-Hassan is pitcher
-Jason is second baseman
-Adam is third baseman
-Charles is catcher

* Ed, Pascal Jason, the right fielder and the centre fielder are bachelors, the others are all married
-Ed, Pascal, and Jason are not the right or center fielders
-Ed, Pascal and Jason can't be third baseman or pitcher
-Sung cannot be right or center fielder, therefore Sung is left fielder
-Adam, Bobo, Charles, Ed, Hassan, Jason, Mathieu, and Pascal are not left fielder
-Bobo is center fielder and Mathieu is right fielder so Adam, Charles, Hassan, and Sung are all married
-Adam, Charles, Hassan, and Sung cannot be second baseman

* The shortstop, the third baseman and Bobo all attended the fight,
-Bobo is not the short stop or the third baseman

* Mathieu is the shortest player of the team,
-Mathieu is not center fielder

Determine the positions of each player on the baseball team.

Note: On a baseball team there are three outfielders (right, centre and left), four infielders (first baseman, second baseman, third baseman and shortstop) and the battery (pitcher and catcher).

==Roland Will's Answers==

Positions
*Catcher: Charles
*Pitcher: Hassan
*First Baseman: Pascal
*Second Baseman: Jason
*Short Stop: Ed
*Third Baseman: Adam
*Right Fielder: Mathieu
*Center Fielder: Bobo
*Left Fielder: Sung

Course:MATH110/Archive/2010-2011/003/Groups/Group 18/Homework October 20th, 2010

2010-10-20T10:28:08Z

RolandWill: /* Roland Will */

==MATH110/003/Groups/Group18HomeworkOctober20th,2010==

==Victoria Wall==
Problem 1
Five persons named their pets after each other. From the following clues, can you decide which pet belongs to Suzan's mother?

Tosh owns a cat,
Bianca owns a frog that she loves,
Jaela owns a parrot which keeps calling her "darling, darling",
Jun owns a snake, don't mess with him,
Suzan is the name of the frog,
The cat is named Jun,
The name by which they call the turtle is the name of the woman whose pet is Tosh,
Finally, Suzan's mother's pet is Bianca.

tosh owns a cat names Jun
bianca owns a frog named suzan
Jun owns a snake named Bianca --- Jun is suzans mother

==Roland Will's work==

Adam, Bobo, Charles, Ed, Hassan, Jason, Mathieu, Pascal and Sung have formed a baseball team. The following facts are true:

* Adam does not like the catcher,
-Adam is not the catcher

* Ed's sister is engaged to the second baseman,
-Ed isn't second baseman
-second baseman is not married

* The centre fielder is taller than the right fielder,
-The center fielder is the 1-8th tallest person
-The right fielder is the 2-9th tallest person

* Hassan and the third baseman live in the same building,
-Hassan isn't 3rd baseman

* Pascal and Charles each won $20 from the pitcher at a poker game,
-Pascal and Charles aren't the pitcher

* Ed and the outfielders play cards during their free time,
-Ed isn't an outfielder

* The pitcher's wife is the third baseman's sister,
-The pitcher is married

* All the battery and infield except Charles, Hassan and Adam are shorter than Sung,
-Charles, Hassan, and Adam are part of the battery or infield, so they are not outfielders
-Sung cannot be shorter than himself and he cannot be Charles, Hassan, or Adam, so Sung is not part of the battery or the infield
-Sung is the 4-8 tallest person
-Charles, Hassan and Adam are the 1-4 tallest people

* Pascal, Adam and the shortstop lost $100 each at the race track,
-Pascal and Adam are not the short stop

* The second baseman beat Pascal, Hassan, Bobo and the catcher at billiards,
-Pascal, Hassan, and Bobo are not the second baseman or the catcher

* Sung is in the process of getting a divorce,
-Sung is married

* The catcher and the third baseman each have two legitimate children,
-The catcher is married
-The third baseman is married
-Bobo, Ed, Jason, Mathieu and Pascal cannot be catcher or third base
-Pascal is first baseman
-Ed is Short Stop
-Hassan is pitcher
-Jason is second baseman
-Adam is third baseman
-Charles is catcher

* Ed, Pascal Jason, the right fielder and the centre fielder are bachelors, the others are all married
-Ed, Pascal, and Jason are not the right or center fielders
-Ed, Pascal and Jason can't be third baseman or pitcher
-Sung cannot be right or center fielder, therefore Sung is left fielder
-Adam, Bobo, Charles, Ed, Hassan, Jason, Mathieu, and Pascal are not left fielder
-Bobo is center fielder and Mathieu is right fielder so Adam, Charles, Hassan, and Sung are all married
-Adam, Charles, Hassan, and Sung cannot be second baseman

* The shortstop, the third baseman and Bobo all attended the fight,
-Bobo is not the short stop or the third baseman

* Mathieu is the shortest player of the team,
-Mathieu is not center fielder

Determine the positions of each player on the baseball team.

Note: On a baseball team there are three outfielders (right, centre and left), four infielders (first baseman, second baseman, third baseman and shortstop) and the battery (pitcher and catcher).

==Answers==

Positions:
*Catcher:
*Pitcher: Ed
*First Baseman:
*Second Baseman:
*Short Stop:
*Third Baseman:
*Right Fielder:
*Center Fielder:
*Left Fielder:

Course:MATH110/Archive/2010-2011/003/Groups/Group 18/Homework October 20th, 2010

2010-10-20T07:02:11Z

RolandWill:

==MATH110/003/Groups/Group18HomeworkOctober20th,2010==

==Roland Will==

Adam, Bobo, Charles, Ed, Hassan, Jason, Mathieu, Pascal and Sung have formed a baseball team. The following facts are true:

* Adam does not like the catcher,

* Ed's sister is engaged to the second baseman,

* The centre fielder is taller than the right fielder,

* Hassan and the third baseman live in the same building,

* Pascal and Charles each won $20 from the pitcher at a poker game,
-Pascal and Charles must be outfielders because Ed is the only non-outfielder that doesn't play cards.

* Ed and the outfielders play cards during their free time,
-Ed must be the pitcher because he is the only non-outfielder who plays cards and Pascal and Charles won $20 from the pitcher in poker

* The pitcher's wife is the third baseman's sister,

* All the battery and infield except Charles, Hassan and Adam are shorter than Sung,

* Pascal, Adam and the shortstop lost $100 each at the race track,

* The second baseman beat Pascal, Hassan, Bobo and the catcher at billiards,

* Sung is in the process of getting a divorce,

* The catcher and the third baseman each have two legitimate children,

* Ed, Pascal Jason, the right fielder and the centre fielder are bachelors, the others are all married

* The shortstop, the third baseman and Bobo all attended the fight,

* Mathieu is the shortest player of the team,

Determine the positions of each player on the baseball team.

Note: On a baseball team there are three outfielders (right, centre and left), four infielders (first baseman, second baseman, third baseman and shortstop) and the battery (pitcher and catcher).

==Answers==

Positions:
*Catcher:
*Pitcher: Ed
*First Baseman:
*Second Baseman:
*Short Stop:
*Third Baseman:
*Right Fielder:
*Center Fielder:
*Left Fielder:

Course:MATH110/Archive/2010-2011/003/Groups/Group 18

2010-10-20T06:22:14Z

RolandWill: /* I created a page for our homework due tomorrow: http://wiki.ubc.ca/MATH110/003/Groups/Group18HomeworkOctober20th,2010 */

{{Infobox MATH110 Groups
| group number = 18
| member 1 = [[User:ChouJuChen|Audrey Chen]]
| member 2 = [[User:SifatHasan|Sifat Hasan]]
| member 3 = [[User:CaitlinLastiwkaFarquharson|Caitlin Lastiwka-Farquharson]]
| member 4 = [[User:VictoriaWall|Victoria Wall]]
| member 5 = [[User:RolandWill|Roland Will]]
| member 6 =
}}

==Homework due October 20th, 2010==

I created a page for our homework due tomorrow: http://wiki.ubc.ca/MATH110/003/Groups/Group18HomeworkOctober20th,2010

-Roland

==1-5==
==Victoria Wall ==
==1.A bus traveled from the terminal to the airport at an average speed of 30 mi/hr and the trip took an hour and 20 min. The bus then traveled from the airport back to the terminal and again averaged 30 mi/hr. However, the return trip required 80 min. Explain.==

' 'Lets call the terminal T and the airport A. If the bus travelled from T to A at 30mi/hr and it took them one hour and 20 mins to get from T to A at this speed, and there are 60 minutes in one hour, it took the bus 60min + 20min to get to A which is a total of 80min. The bus took 80 min to get from T to A. To get from A to T at the same speed (30mi/hr) it took the bus 80min. 80min = 80 min. This means going from A to T or vis versa at 30 mi/hr it will take the bus 80min.

==2.A lady did not have her driver's license with her when she failed to stop at a stop sign and then went three blocks down a one-way street the wrong way. A policeman saw her, but he did not stop her. Explain. ==

' 'The lady was walking. It never says she was driving.

==3.One of three boxes contains apples, another box contains oranges, and another box contains a mixture of apples and oranges. The boxes are labeled APPLES, ORANGES and APPLES AND ORANGES, but each label is incorrect. Can you select one fruit from only one box and determine the correct labels? Explain. ==

' 'if you selecet from the box APPLES AND ORANGES then you will be able to see the labels if they are correct or not.

==4.I am the brother of the blind fiddler, but brothers I have none. How can this be? ==

' 'Since it says that he is the brother of the blind fiddler it does not mean that the fiddle is male, since he has no brothers than the fiddler must be a female.

==5.Two quarters rest next to each other on a table. One coin is held fixed while the second coin is rolled around the edge of the first coin with no slipping. When the moving coin returns to its original position, how many times has it revolved? ==

' 'This is because the moving quarters revolves two full revolutions

==6-10==
== Caitlin Lastiwka- Farquharson ==

==6. Three kinds of apples are all mixed up in a basket. How many apples must you draw without (without looking) from the basket to be sure of getting at least two of a kind? ==

' ' To be sure you are getting at least two of a kind, you must select all of the other types of apples, plus two more. Meaning that only once you have selected all of the other apples can you be sure that you will select two of the kind you desire. It can be written like this: x,a x2, b and x3, c, with x representing the quantity of apples. This can be calculated by x2 + x3 +2. X2 representing one of the types of apples, x3 representing the other type and 2 representing 2 of the kind of apples you are trying to select. This is the only way to be sure you are getting at least two of a kind. ' '

==7. Suppose you have 40 blue socks and 40 brown socks in a drawer. How many socks must you take from the drawer (without looking) to be sure of getting (i) a pair of the same colour, and (ii) a pair with different colors. ==

' 'You must take three socks from the drawer to ensure you have a pair that match. This is because if you only select two, one could be brown and one could be blue. Selecting three, ensures that at least two of them will be the same colour. As for part two, you would need to select 41 socks to ensure you had a pair of different coloured socks because if you select 40 or less you could get all the same colour, but selecting 41 ensures you will have at least one pair of mixed colour. ' '

==8. Rueben says "Two days ago I was 20 years old. Later next year I will be 23 years old." Explain how this is possible. ==

' 'It is possible if your birthday is on the 31st of December and today is the 1st of January. This is because on the 30th of December (two days ago) you we’re 20 years old and now you are 21, later this year you will turn 22 on the 31st of December, and therefore 23 the next year.' '

==9. A rope ladder hanging over the side of a boat has rungs one foot apart. Ten rungs are showing. If the tide rises five feet, how many rungs will be showing? ==

' ' 5 rungs will be showing, because if there are 10 showing now, and they are each a foot apart, then for 5 more rungs to be showing there would need to be an increase in the level of water by 5 feet. ' '

==10.Suppose one-half of all people are chocolate eaters and one-half of all people are women. (i) Does it follow that one-fourth of all people are women chocolate eaters? (ii) Does it follow that one-half of all men are chocolate eaters? Explain. ==

' ' No, it does not follow that one-fourth of all people are women chocolate eaters and it does not follow that half of all men are chocolate eaters because are completely independent scenarios. Meaning that the the amount of women there are does not influence the amount of men that will eat chocolate. For example, If 50% of people are women and 50% of the entire population including men and women eat chocolate (arrived at by using the same logic that if 1/4 of women eat chocolate and 1/4 of men eat chocolate), that entire 50% could be comprised of women, meaning that no men eat chocolate disproving the statement.

==11-14==
==Sifat Hasan==

==11 11. A woman, her older brother, her son, and her daughter are chess players. The worst player’s twin, who is one of the four players, and the best player are of opposite sex. The worst player and the best player have the same age. If this is possible, who is the worst player?==

The four players (according to age, from oldest to youngest) are: woman's older brother, woman, and the son and the daughter (of the same age). Assuming that the children are of the same age (i.e. twins), the worst player is one of them, since they are the only ones who can have a twin. Assuming that the worst player is the daughter, her brother the son, is of the opposite sex as the woman, therefore the woman is the worst player. However, since the worst and the best player are of the same age, this is not possible, because the twins are of the opposite sex and they are of different genders.

==12 A Manhattan fellow had a girlfriend in the Bronx and a girlfriend in Brooklyn. He decided which girlfriend to visit by arriving randomly at the train station and taking the first of the Bronx or Brooklyn trains that arrived. The trains to Brooklyn and the Bronx each arrived regularly every 10 minutes. Not long after he began his scheme the man's Bronx girlfriend left him because he rarely visited. Give a (logical) explanation==

Assuming that the Bronx and the Brooklyn train arrive one after the other every 10 minutes, the only logical explanation would be that the man in Manhattan coincidentally went to the station 10 minutes or less before a train to Brooklyn arrived, most of the time.

==13 If a clock takes 5 seconds to strike 5:00 (with 5 equally spaced chimes), how long does it take to strike 10:00 (with 10 equally spaced chimes)?==

If it takes 5 seconds to strike 5, there will be 4 little halts in the middle. Therefore it takes 5 chimes 4 (5/4) = 1.25 second halts to finish. For 10 chimes, there are 9 halts so, it takes 9x 1.25 = 11.25 seconds for 10 halts.

==14 One day in the maternity ward, the name tags for four girl babies became mixed up. (i) In how many different ways could two of the babies be tagged correctly and two of the babies be tagged incorrectly? (ii) In how many different ways could three of the babies be tagged correctly and one baby be tagged incorrectly?==

(i)and (ii) If we take the babies names as A,B,C and D. There are 6 different combinations of the mix up, that two babies' names can be correct and 2 can be wrong. Assuming the name tags for the babies A,B,C and D are in respective order, they are ABDC, ADCB, ACBD, DBCA, CBAD and BACD. All other combinations for example BCAD will have one correct and 3 incorrect, or all four of them correct, because if 3 are correct, the fourth one has to be correct.

==15-16==
==Roland Will==

==15. Alex says to you, “I'll bet you any amount of money that if I shuffle this deck of cards, there will always be as many red cards in the first half of the deck as there are black cards in the second half of the deck.” Should you accept his bet?==

Answer: No, you shouldn't assuming the deck has equal amounts of red and black cards as in a standard 52 card deck.
Solution: In a standard 52 card deck, half of the cards (26) are black and half are red. If you take 26 cards at random from the deck, x of them will be black and y of them will be red, and x+y=26. As there are 26 of each color in the deck, then x+?=26 for the black cards in the deck and ?+y=26 for the red cards in the deck. As x+y=26 in the first randomly selected 26 cards, then the value of black cards in the other half of the deck must equal y, and the value of red cards in the other half of the deck must equal x meaning that "there will always be as many red cards in the first half of the deck as there are black cards in the second half of the deck."

==16. Suppose that each daughter in your family has the same number of brothers as she has sisters, and each son in your family has twice as many sisters as he has brothers. How many sons and daughters are in the family?==

Answer:3 total, 2 sister and 1 brother
Solution: Since the daughters in the family each have as many brothers as sisters the amount of sisters, with x standing for the amount of brothers, is x+1. As each brother has twice as many sisters as brothers, the amount of sisters must equal 2(x-1) or 2x-2. To find the number of brother: x+1=2x+1, 1=x-2, 3=x, which means that their are 3 brothers and 4 sisters (x+1= the number of sisters and x=3). This makes sense because a sister would have an equal amount of brothers to sisters, 3 sisters and 3 brothers, if there were 4 sisters and 3 brothers total, and each brother would have 4 sisters and 3 brothers, which is twice the amount of brothers to sisters.

==17~21==
==Audrey Chen==

==17.The zero point on a bathroom scale is set incorrectly, but otherwise the scale is accurate. It shows 60 kg when Dan stands on the scale, 50 kg when Sarah stands on the scale, but 105 kg when Dan and Sarah both stand on the scale. Does the scale read too high or too low? Explain. ==

''The scale read too low, since Dan is shown as 60kg and Sarah is 50kg, suppose 60+50=110, 105-110=-5, so that means the scale is smaller than 0 in the beginning''

==18. Alice takes one-third of the pennies from a large jar. Then Bret takes one-third of the remaining pennies from the jar. Finally, Carla takes one-third of the remaining pennies from the jar, leaving 40 pennies in the jar. How many pennies were in the jar at the start? ==

''If the total pennies is "x", Alice take 1/3x, so it has 2/3x left after Alice took it, than Bret take 1/3 out, after Alice took it, which is 2/3x*1/3= 2/9x, so in the beginning they have x, after Alice took it, it has 2/3x left, and Bret took 2/9x, so after Bret took it, it becomes 2/3x-2/9x= 4/9x-2/9x=2/9x left in the jar. Than Carla take 1/3 of the rest, so she took 1/3 of rest which is 2/9x*1/3=3/27x, so Alice took 1/3x, Bret tool 2/9x, Carla took 3/27x, three of them totaly took 1/3x+2/9x+3/27x=18/27x, so there still has x-18/27x= 9/27x= 1/3 left, 1/3x=40pennies, so x=120 pennies, so it was having 120 pennies in the jar.

==19. One morning each member of Angela's family drank an eight-ounce cup of coffee and milk, with the (nonzero) amounts of coffee and milk varying from cup to cup. Angela drank a quarter of the total amount of milk and a sixth of the total amount of coffee. What is the least number of people in the family? ==

''If we let total milk is x, total coffee is y. Than 1/4x+1/6y=8, and because every cup is 8ounce, x+y is multiple by 8. So make it easier, we use 1/4x+1/6y=8 * 12 to both sides. than we will got 3x+2y=96, now we have 3x+2y=96 and x+y is multiple of 8, and the number that multiple by 8 is 8, 16, 24, 32... so 2x+2y= 16, 32, 48, 64, 80, 96, since 3x+2y=96, it can't be more than 96. It will only have 6 possible number, so if you take 3x+2y=96 substracting 2x+2y=16, 32, 48, 64, 80, 96 you can get 6 possible x, which are 80, 64, 48, 32, 16, and 0. Than put the number into 3x+2y=96, if you put 80 in, will get 20, which is bigger than 8, and also 64, 48. If we use 32, it will equal to 8, but that means we have 0 coffee, but coffee can't be 0, so there's only 16 and 0 left. Since Angela had 1/4 of total amount of milk, milk can't be 0. So we got 16ounce than 16*(1/4)=4, so that means she had 8-4=4 's coffee. So 4=1/6 coffee, than the total amount of coffee would be 4*6=24. than x=16 and y=24, 16+24=40 40/8ounce=5, so at least have 5 cups of drinks, so that means at least they have 5 members in Angela's family.''

==20.Of two clocks next to each other, one runs 5 min per hour fast and the other runs 5 min per hour slow. At midnight the clocks show the same time. At what time are they are one hour apart? ==

''Since one clock runs 5 min faster per hour, the other is 5 min slower, after clock runs an hour, two clocks will have 10 min different from each other. 60 min an hour. 60/10=6, so after 6 hours two clocks will having one hour apart, and that would be 6AM.''

==21.Sven placed exactly in the middle among all runners in a race. Dan was slower than Sven, in 10th place, and Lars was in 16th place. How many runners were in the race? ==

''There were 17 runners. Since lars was in 16th place, the runners at least have to be 16, than if Sven is placed exactly in the middle, it means it would have even number of runners. Because Dan is slower and he was at 10 place that tells us Seven has to be before 10th, and if there has 19 runners, Sven and Dan would be at the same place, so it should be 17 runners, than Sven would be at exactly in the middle which at 9th place.''

==22-25==

==Roland Will==

==22. During a vacation, it rained on 13 days, but when it rained in the morning, the afternoon was sunny, and every rainy afternoon was preceded by a sunny morning. There were 11 sunny mornings and 12 sunny afternoons. How long was the vacation?==

Answer: 18 days of vacation.

Solution: 13 of the days of vacation were half sunny and half rainy. As there were 23 sunny mornings and afternoons (11 sunny mornings+12 sunny afternoons = 23 sunny mornings and afternoons), 13 of those sunny afternoons or mornings were on half rainy days. This means there are 10 sunny half-days left over, which equal 5 sunny full days. The 5 sunny full days plus the 13 half sunny/rainy days equal 18 total days of vacation.

==23. Suppose you overhear the following conversation: Paul: How old are your three children? Paula: The product of their ages is 36 and the sum of their ages is the same as today's date. Paul: That is not enough information. Paula: The oldest child also has red hair. If you were Paul could you determine the ages of Paula's children? Explain.==

Answer: If I were Paul this might be possible, but since we don’t know the date that Paula said this, it is not possible for us to find out.

Solution: There are many different combinations of three numbers that can be multiplied and will produce 36. As we do not know the date that Paula said this, the only thing we can be sure of is that the sum of the ages is less than 31 because no month has more than 31 days. Unfortunately, only one set of ages (ages 1 year old, 1 year old and 36 years old) has a sum greater than 31, which leaves many possible combinations open as possible. For today’s date, the 13th, ages of 2, 2, and 9 would produce 36 and have a sum of 13, but, again, it is uncertain. If it were the first of the month, there would be no possible combinations that would produce 36 and sum 1.

==24. Two candles of equal length were lit at the same time. One candle took 6 hr to burn out and the other candle took 3 hr to burn out. After how much time was one candle exactly twice as long as the other candle?==

Answer: 2 hours.

Solution: The faster burning candle took half the time to burn as the slower burning candle (3 hours/ 6 hours = 1/2), meaning it burned twice as fast. This means that after 2/3 of the total burning time for the faster burning candle it will be 1/3 of its original height and at the slower burning candle will be at 2/3 of its original height and 1/3 is half of 2/3. Since the faster burning candle took 3 hours to burn, 2/3 of its total burning time is 2 hours.

==25. Two candles of length L and L + 1 were lit at 6:00 and 4:30, respectively. At 8:30 they had the same length. The longer candle died at 10:30 and the shorter candle died at 10:00. Find L.==

Answer: L=2.

Solution: The shorter candle lasted for 4 hours and the longer candle lasted for 6 hours. As 6 hours – 4 hours = 2 hours and 2 hours / 4 hours = 1/2, the longer candle lasted 50% longer and was, therefore, 50% longer in length. This means that the +1 in L+1 on the longer candle was 1/2 of L. 1/2L=1, so L=2*1, L=2.

Course:MATH110/Archive/2010-2011/003/Groups/Group 18

2010-10-20T06:21:16Z

RolandWill: /* I created a page for our homework due tomorrow: http://wiki.ubc.ca/MATH110/003/Groups/Group18HomeworkOctober20th,2010 */

{{Infobox MATH110 Groups
| group number = 18
| member 1 = [[User:ChouJuChen|Audrey Chen]]
| member 2 = [[User:SifatHasan|Sifat Hasan]]
| member 3 = [[User:CaitlinLastiwkaFarquharson|Caitlin Lastiwka-Farquharson]]
| member 4 = [[User:VictoriaWall|Victoria Wall]]
| member 5 = [[User:RolandWill|Roland Will]]
| member 6 =
}}

==I created a page for our homework due tomorrow: http://wiki.ubc.ca/MATH110/003/Groups/Group18HomeworkOctober20th,2010==

-Roland

==1-5==
==Victoria Wall ==
==1.A bus traveled from the terminal to the airport at an average speed of 30 mi/hr and the trip took an hour and 20 min. The bus then traveled from the airport back to the terminal and again averaged 30 mi/hr. However, the return trip required 80 min. Explain.==

' 'Lets call the terminal T and the airport A. If the bus travelled from T to A at 30mi/hr and it took them one hour and 20 mins to get from T to A at this speed, and there are 60 minutes in one hour, it took the bus 60min + 20min to get to A which is a total of 80min. The bus took 80 min to get from T to A. To get from A to T at the same speed (30mi/hr) it took the bus 80min. 80min = 80 min. This means going from A to T or vis versa at 30 mi/hr it will take the bus 80min.

==2.A lady did not have her driver's license with her when she failed to stop at a stop sign and then went three blocks down a one-way street the wrong way. A policeman saw her, but he did not stop her. Explain. ==

' 'The lady was walking. It never says she was driving.

==3.One of three boxes contains apples, another box contains oranges, and another box contains a mixture of apples and oranges. The boxes are labeled APPLES, ORANGES and APPLES AND ORANGES, but each label is incorrect. Can you select one fruit from only one box and determine the correct labels? Explain. ==

' 'if you selecet from the box APPLES AND ORANGES then you will be able to see the labels if they are correct or not.

==4.I am the brother of the blind fiddler, but brothers I have none. How can this be? ==

' 'Since it says that he is the brother of the blind fiddler it does not mean that the fiddle is male, since he has no brothers than the fiddler must be a female.

==5.Two quarters rest next to each other on a table. One coin is held fixed while the second coin is rolled around the edge of the first coin with no slipping. When the moving coin returns to its original position, how many times has it revolved? ==

' 'This is because the moving quarters revolves two full revolutions

==6-10==
== Caitlin Lastiwka- Farquharson ==

==6. Three kinds of apples are all mixed up in a basket. How many apples must you draw without (without looking) from the basket to be sure of getting at least two of a kind? ==

' ' To be sure you are getting at least two of a kind, you must select all of the other types of apples, plus two more. Meaning that only once you have selected all of the other apples can you be sure that you will select two of the kind you desire. It can be written like this: x,a x2, b and x3, c, with x representing the quantity of apples. This can be calculated by x2 + x3 +2. X2 representing one of the types of apples, x3 representing the other type and 2 representing 2 of the kind of apples you are trying to select. This is the only way to be sure you are getting at least two of a kind. ' '

==7. Suppose you have 40 blue socks and 40 brown socks in a drawer. How many socks must you take from the drawer (without looking) to be sure of getting (i) a pair of the same colour, and (ii) a pair with different colors. ==

' 'You must take three socks from the drawer to ensure you have a pair that match. This is because if you only select two, one could be brown and one could be blue. Selecting three, ensures that at least two of them will be the same colour. As for part two, you would need to select 41 socks to ensure you had a pair of different coloured socks because if you select 40 or less you could get all the same colour, but selecting 41 ensures you will have at least one pair of mixed colour. ' '

==8. Rueben says "Two days ago I was 20 years old. Later next year I will be 23 years old." Explain how this is possible. ==

' 'It is possible if your birthday is on the 31st of December and today is the 1st of January. This is because on the 30th of December (two days ago) you we’re 20 years old and now you are 21, later this year you will turn 22 on the 31st of December, and therefore 23 the next year.' '

==9. A rope ladder hanging over the side of a boat has rungs one foot apart. Ten rungs are showing. If the tide rises five feet, how many rungs will be showing? ==

' ' 5 rungs will be showing, because if there are 10 showing now, and they are each a foot apart, then for 5 more rungs to be showing there would need to be an increase in the level of water by 5 feet. ' '

==10.Suppose one-half of all people are chocolate eaters and one-half of all people are women. (i) Does it follow that one-fourth of all people are women chocolate eaters? (ii) Does it follow that one-half of all men are chocolate eaters? Explain. ==

' ' No, it does not follow that one-fourth of all people are women chocolate eaters and it does not follow that half of all men are chocolate eaters because are completely independent scenarios. Meaning that the the amount of women there are does not influence the amount of men that will eat chocolate. For example, If 50% of people are women and 50% of the entire population including men and women eat chocolate (arrived at by using the same logic that if 1/4 of women eat chocolate and 1/4 of men eat chocolate), that entire 50% could be comprised of women, meaning that no men eat chocolate disproving the statement.

==11-14==
==Sifat Hasan==

==11 11. A woman, her older brother, her son, and her daughter are chess players. The worst player’s twin, who is one of the four players, and the best player are of opposite sex. The worst player and the best player have the same age. If this is possible, who is the worst player?==

The four players (according to age, from oldest to youngest) are: woman's older brother, woman, and the son and the daughter (of the same age). Assuming that the children are of the same age (i.e. twins), the worst player is one of them, since they are the only ones who can have a twin. Assuming that the worst player is the daughter, her brother the son, is of the opposite sex as the woman, therefore the woman is the worst player. However, since the worst and the best player are of the same age, this is not possible, because the twins are of the opposite sex and they are of different genders.

==12 A Manhattan fellow had a girlfriend in the Bronx and a girlfriend in Brooklyn. He decided which girlfriend to visit by arriving randomly at the train station and taking the first of the Bronx or Brooklyn trains that arrived. The trains to Brooklyn and the Bronx each arrived regularly every 10 minutes. Not long after he began his scheme the man's Bronx girlfriend left him because he rarely visited. Give a (logical) explanation==

Assuming that the Bronx and the Brooklyn train arrive one after the other every 10 minutes, the only logical explanation would be that the man in Manhattan coincidentally went to the station 10 minutes or less before a train to Brooklyn arrived, most of the time.

==13 If a clock takes 5 seconds to strike 5:00 (with 5 equally spaced chimes), how long does it take to strike 10:00 (with 10 equally spaced chimes)?==

If it takes 5 seconds to strike 5, there will be 4 little halts in the middle. Therefore it takes 5 chimes 4 (5/4) = 1.25 second halts to finish. For 10 chimes, there are 9 halts so, it takes 9x 1.25 = 11.25 seconds for 10 halts.

==14 One day in the maternity ward, the name tags for four girl babies became mixed up. (i) In how many different ways could two of the babies be tagged correctly and two of the babies be tagged incorrectly? (ii) In how many different ways could three of the babies be tagged correctly and one baby be tagged incorrectly?==

(i)and (ii) If we take the babies names as A,B,C and D. There are 6 different combinations of the mix up, that two babies' names can be correct and 2 can be wrong. Assuming the name tags for the babies A,B,C and D are in respective order, they are ABDC, ADCB, ACBD, DBCA, CBAD and BACD. All other combinations for example BCAD will have one correct and 3 incorrect, or all four of them correct, because if 3 are correct, the fourth one has to be correct.

==15-16==
==Roland Will==

==15. Alex says to you, “I'll bet you any amount of money that if I shuffle this deck of cards, there will always be as many red cards in the first half of the deck as there are black cards in the second half of the deck.” Should you accept his bet?==

Answer: No, you shouldn't assuming the deck has equal amounts of red and black cards as in a standard 52 card deck.
Solution: In a standard 52 card deck, half of the cards (26) are black and half are red. If you take 26 cards at random from the deck, x of them will be black and y of them will be red, and x+y=26. As there are 26 of each color in the deck, then x+?=26 for the black cards in the deck and ?+y=26 for the red cards in the deck. As x+y=26 in the first randomly selected 26 cards, then the value of black cards in the other half of the deck must equal y, and the value of red cards in the other half of the deck must equal x meaning that "there will always be as many red cards in the first half of the deck as there are black cards in the second half of the deck."

==16. Suppose that each daughter in your family has the same number of brothers as she has sisters, and each son in your family has twice as many sisters as he has brothers. How many sons and daughters are in the family?==

Answer:3 total, 2 sister and 1 brother
Solution: Since the daughters in the family each have as many brothers as sisters the amount of sisters, with x standing for the amount of brothers, is x+1. As each brother has twice as many sisters as brothers, the amount of sisters must equal 2(x-1) or 2x-2. To find the number of brother: x+1=2x+1, 1=x-2, 3=x, which means that their are 3 brothers and 4 sisters (x+1= the number of sisters and x=3). This makes sense because a sister would have an equal amount of brothers to sisters, 3 sisters and 3 brothers, if there were 4 sisters and 3 brothers total, and each brother would have 4 sisters and 3 brothers, which is twice the amount of brothers to sisters.

==17~21==
==Audrey Chen==

==17.The zero point on a bathroom scale is set incorrectly, but otherwise the scale is accurate. It shows 60 kg when Dan stands on the scale, 50 kg when Sarah stands on the scale, but 105 kg when Dan and Sarah both stand on the scale. Does the scale read too high or too low? Explain. ==

''The scale read too low, since Dan is shown as 60kg and Sarah is 50kg, suppose 60+50=110, 105-110=-5, so that means the scale is smaller than 0 in the beginning''

==18. Alice takes one-third of the pennies from a large jar. Then Bret takes one-third of the remaining pennies from the jar. Finally, Carla takes one-third of the remaining pennies from the jar, leaving 40 pennies in the jar. How many pennies were in the jar at the start? ==

''If the total pennies is "x", Alice take 1/3x, so it has 2/3x left after Alice took it, than Bret take 1/3 out, after Alice took it, which is 2/3x*1/3= 2/9x, so in the beginning they have x, after Alice took it, it has 2/3x left, and Bret took 2/9x, so after Bret took it, it becomes 2/3x-2/9x= 4/9x-2/9x=2/9x left in the jar. Than Carla take 1/3 of the rest, so she took 1/3 of rest which is 2/9x*1/3=3/27x, so Alice took 1/3x, Bret tool 2/9x, Carla took 3/27x, three of them totaly took 1/3x+2/9x+3/27x=18/27x, so there still has x-18/27x= 9/27x= 1/3 left, 1/3x=40pennies, so x=120 pennies, so it was having 120 pennies in the jar.

==19. One morning each member of Angela's family drank an eight-ounce cup of coffee and milk, with the (nonzero) amounts of coffee and milk varying from cup to cup. Angela drank a quarter of the total amount of milk and a sixth of the total amount of coffee. What is the least number of people in the family? ==

''If we let total milk is x, total coffee is y. Than 1/4x+1/6y=8, and because every cup is 8ounce, x+y is multiple by 8. So make it easier, we use 1/4x+1/6y=8 * 12 to both sides. than we will got 3x+2y=96, now we have 3x+2y=96 and x+y is multiple of 8, and the number that multiple by 8 is 8, 16, 24, 32... so 2x+2y= 16, 32, 48, 64, 80, 96, since 3x+2y=96, it can't be more than 96. It will only have 6 possible number, so if you take 3x+2y=96 substracting 2x+2y=16, 32, 48, 64, 80, 96 you can get 6 possible x, which are 80, 64, 48, 32, 16, and 0. Than put the number into 3x+2y=96, if you put 80 in, will get 20, which is bigger than 8, and also 64, 48. If we use 32, it will equal to 8, but that means we have 0 coffee, but coffee can't be 0, so there's only 16 and 0 left. Since Angela had 1/4 of total amount of milk, milk can't be 0. So we got 16ounce than 16*(1/4)=4, so that means she had 8-4=4 's coffee. So 4=1/6 coffee, than the total amount of coffee would be 4*6=24. than x=16 and y=24, 16+24=40 40/8ounce=5, so at least have 5 cups of drinks, so that means at least they have 5 members in Angela's family.''

==20.Of two clocks next to each other, one runs 5 min per hour fast and the other runs 5 min per hour slow. At midnight the clocks show the same time. At what time are they are one hour apart? ==

''Since one clock runs 5 min faster per hour, the other is 5 min slower, after clock runs an hour, two clocks will have 10 min different from each other. 60 min an hour. 60/10=6, so after 6 hours two clocks will having one hour apart, and that would be 6AM.''

==21.Sven placed exactly in the middle among all runners in a race. Dan was slower than Sven, in 10th place, and Lars was in 16th place. How many runners were in the race? ==

''There were 17 runners. Since lars was in 16th place, the runners at least have to be 16, than if Sven is placed exactly in the middle, it means it would have even number of runners. Because Dan is slower and he was at 10 place that tells us Seven has to be before 10th, and if there has 19 runners, Sven and Dan would be at the same place, so it should be 17 runners, than Sven would be at exactly in the middle which at 9th place.''

==22-25==

==Roland Will==

==22. During a vacation, it rained on 13 days, but when it rained in the morning, the afternoon was sunny, and every rainy afternoon was preceded by a sunny morning. There were 11 sunny mornings and 12 sunny afternoons. How long was the vacation?==

Answer: 18 days of vacation.

Solution: 13 of the days of vacation were half sunny and half rainy. As there were 23 sunny mornings and afternoons (11 sunny mornings+12 sunny afternoons = 23 sunny mornings and afternoons), 13 of those sunny afternoons or mornings were on half rainy days. This means there are 10 sunny half-days left over, which equal 5 sunny full days. The 5 sunny full days plus the 13 half sunny/rainy days equal 18 total days of vacation.

==23. Suppose you overhear the following conversation: Paul: How old are your three children? Paula: The product of their ages is 36 and the sum of their ages is the same as today's date. Paul: That is not enough information. Paula: The oldest child also has red hair. If you were Paul could you determine the ages of Paula's children? Explain.==

Answer: If I were Paul this might be possible, but since we don’t know the date that Paula said this, it is not possible for us to find out.

Solution: There are many different combinations of three numbers that can be multiplied and will produce 36. As we do not know the date that Paula said this, the only thing we can be sure of is that the sum of the ages is less than 31 because no month has more than 31 days. Unfortunately, only one set of ages (ages 1 year old, 1 year old and 36 years old) has a sum greater than 31, which leaves many possible combinations open as possible. For today’s date, the 13th, ages of 2, 2, and 9 would produce 36 and have a sum of 13, but, again, it is uncertain. If it were the first of the month, there would be no possible combinations that would produce 36 and sum 1.

==24. Two candles of equal length were lit at the same time. One candle took 6 hr to burn out and the other candle took 3 hr to burn out. After how much time was one candle exactly twice as long as the other candle?==

Answer: 2 hours.

Solution: The faster burning candle took half the time to burn as the slower burning candle (3 hours/ 6 hours = 1/2), meaning it burned twice as fast. This means that after 2/3 of the total burning time for the faster burning candle it will be 1/3 of its original height and at the slower burning candle will be at 2/3 of its original height and 1/3 is half of 2/3. Since the faster burning candle took 3 hours to burn, 2/3 of its total burning time is 2 hours.

==25. Two candles of length L and L + 1 were lit at 6:00 and 4:30, respectively. At 8:30 they had the same length. The longer candle died at 10:30 and the shorter candle died at 10:00. Find L.==

Answer: L=2.

Solution: The shorter candle lasted for 4 hours and the longer candle lasted for 6 hours. As 6 hours – 4 hours = 2 hours and 2 hours / 4 hours = 1/2, the longer candle lasted 50% longer and was, therefore, 50% longer in length. This means that the +1 in L+1 on the longer candle was 1/2 of L. 1/2L=1, so L=2*1, L=2.

Course:MATH110/Archive/2010-2011/003/Groups/Group 18

2010-10-20T06:20:54Z

RolandWill:

{{Infobox MATH110 Groups
| group number = 18
| member 1 = [[User:ChouJuChen|Audrey Chen]]
| member 2 = [[User:SifatHasan|Sifat Hasan]]
| member 3 = [[User:CaitlinLastiwkaFarquharson|Caitlin Lastiwka-Farquharson]]
| member 4 = [[User:VictoriaWall|Victoria Wall]]
| member 5 = [[User:RolandWill|Roland Will]]
| member 6 =
}}

==I created a page for our homework due tomorrow: http://wiki.ubc.ca/MATH110/003/Groups/Group18HomeworkOctober20th,2010==

==1-5==
==Victoria Wall ==
==1.A bus traveled from the terminal to the airport at an average speed of 30 mi/hr and the trip took an hour and 20 min. The bus then traveled from the airport back to the terminal and again averaged 30 mi/hr. However, the return trip required 80 min. Explain.==

' 'Lets call the terminal T and the airport A. If the bus travelled from T to A at 30mi/hr and it took them one hour and 20 mins to get from T to A at this speed, and there are 60 minutes in one hour, it took the bus 60min + 20min to get to A which is a total of 80min. The bus took 80 min to get from T to A. To get from A to T at the same speed (30mi/hr) it took the bus 80min. 80min = 80 min. This means going from A to T or vis versa at 30 mi/hr it will take the bus 80min.

==2.A lady did not have her driver's license with her when she failed to stop at a stop sign and then went three blocks down a one-way street the wrong way. A policeman saw her, but he did not stop her. Explain. ==

' 'The lady was walking. It never says she was driving.

==3.One of three boxes contains apples, another box contains oranges, and another box contains a mixture of apples and oranges. The boxes are labeled APPLES, ORANGES and APPLES AND ORANGES, but each label is incorrect. Can you select one fruit from only one box and determine the correct labels? Explain. ==

' 'if you selecet from the box APPLES AND ORANGES then you will be able to see the labels if they are correct or not.

==4.I am the brother of the blind fiddler, but brothers I have none. How can this be? ==

' 'Since it says that he is the brother of the blind fiddler it does not mean that the fiddle is male, since he has no brothers than the fiddler must be a female.

==5.Two quarters rest next to each other on a table. One coin is held fixed while the second coin is rolled around the edge of the first coin with no slipping. When the moving coin returns to its original position, how many times has it revolved? ==

' 'This is because the moving quarters revolves two full revolutions

==6-10==
== Caitlin Lastiwka- Farquharson ==

==6. Three kinds of apples are all mixed up in a basket. How many apples must you draw without (without looking) from the basket to be sure of getting at least two of a kind? ==

' ' To be sure you are getting at least two of a kind, you must select all of the other types of apples, plus two more. Meaning that only once you have selected all of the other apples can you be sure that you will select two of the kind you desire. It can be written like this: x,a x2, b and x3, c, with x representing the quantity of apples. This can be calculated by x2 + x3 +2. X2 representing one of the types of apples, x3 representing the other type and 2 representing 2 of the kind of apples you are trying to select. This is the only way to be sure you are getting at least two of a kind. ' '

==7. Suppose you have 40 blue socks and 40 brown socks in a drawer. How many socks must you take from the drawer (without looking) to be sure of getting (i) a pair of the same colour, and (ii) a pair with different colors. ==

' 'You must take three socks from the drawer to ensure you have a pair that match. This is because if you only select two, one could be brown and one could be blue. Selecting three, ensures that at least two of them will be the same colour. As for part two, you would need to select 41 socks to ensure you had a pair of different coloured socks because if you select 40 or less you could get all the same colour, but selecting 41 ensures you will have at least one pair of mixed colour. ' '

==8. Rueben says "Two days ago I was 20 years old. Later next year I will be 23 years old." Explain how this is possible. ==

' 'It is possible if your birthday is on the 31st of December and today is the 1st of January. This is because on the 30th of December (two days ago) you we’re 20 years old and now you are 21, later this year you will turn 22 on the 31st of December, and therefore 23 the next year.' '

==9. A rope ladder hanging over the side of a boat has rungs one foot apart. Ten rungs are showing. If the tide rises five feet, how many rungs will be showing? ==

' ' 5 rungs will be showing, because if there are 10 showing now, and they are each a foot apart, then for 5 more rungs to be showing there would need to be an increase in the level of water by 5 feet. ' '

==10.Suppose one-half of all people are chocolate eaters and one-half of all people are women. (i) Does it follow that one-fourth of all people are women chocolate eaters? (ii) Does it follow that one-half of all men are chocolate eaters? Explain. ==

' ' No, it does not follow that one-fourth of all people are women chocolate eaters and it does not follow that half of all men are chocolate eaters because are completely independent scenarios. Meaning that the the amount of women there are does not influence the amount of men that will eat chocolate. For example, If 50% of people are women and 50% of the entire population including men and women eat chocolate (arrived at by using the same logic that if 1/4 of women eat chocolate and 1/4 of men eat chocolate), that entire 50% could be comprised of women, meaning that no men eat chocolate disproving the statement.

==11-14==
==Sifat Hasan==

==11 11. A woman, her older brother, her son, and her daughter are chess players. The worst player’s twin, who is one of the four players, and the best player are of opposite sex. The worst player and the best player have the same age. If this is possible, who is the worst player?==

The four players (according to age, from oldest to youngest) are: woman's older brother, woman, and the son and the daughter (of the same age). Assuming that the children are of the same age (i.e. twins), the worst player is one of them, since they are the only ones who can have a twin. Assuming that the worst player is the daughter, her brother the son, is of the opposite sex as the woman, therefore the woman is the worst player. However, since the worst and the best player are of the same age, this is not possible, because the twins are of the opposite sex and they are of different genders.

==12 A Manhattan fellow had a girlfriend in the Bronx and a girlfriend in Brooklyn. He decided which girlfriend to visit by arriving randomly at the train station and taking the first of the Bronx or Brooklyn trains that arrived. The trains to Brooklyn and the Bronx each arrived regularly every 10 minutes. Not long after he began his scheme the man's Bronx girlfriend left him because he rarely visited. Give a (logical) explanation==

Assuming that the Bronx and the Brooklyn train arrive one after the other every 10 minutes, the only logical explanation would be that the man in Manhattan coincidentally went to the station 10 minutes or less before a train to Brooklyn arrived, most of the time.

==13 If a clock takes 5 seconds to strike 5:00 (with 5 equally spaced chimes), how long does it take to strike 10:00 (with 10 equally spaced chimes)?==

If it takes 5 seconds to strike 5, there will be 4 little halts in the middle. Therefore it takes 5 chimes 4 (5/4) = 1.25 second halts to finish. For 10 chimes, there are 9 halts so, it takes 9x 1.25 = 11.25 seconds for 10 halts.

==14 One day in the maternity ward, the name tags for four girl babies became mixed up. (i) In how many different ways could two of the babies be tagged correctly and two of the babies be tagged incorrectly? (ii) In how many different ways could three of the babies be tagged correctly and one baby be tagged incorrectly?==

(i)and (ii) If we take the babies names as A,B,C and D. There are 6 different combinations of the mix up, that two babies' names can be correct and 2 can be wrong. Assuming the name tags for the babies A,B,C and D are in respective order, they are ABDC, ADCB, ACBD, DBCA, CBAD and BACD. All other combinations for example BCAD will have one correct and 3 incorrect, or all four of them correct, because if 3 are correct, the fourth one has to be correct.

==15-16==
==Roland Will==

==15. Alex says to you, “I'll bet you any amount of money that if I shuffle this deck of cards, there will always be as many red cards in the first half of the deck as there are black cards in the second half of the deck.” Should you accept his bet?==

Answer: No, you shouldn't assuming the deck has equal amounts of red and black cards as in a standard 52 card deck.
Solution: In a standard 52 card deck, half of the cards (26) are black and half are red. If you take 26 cards at random from the deck, x of them will be black and y of them will be red, and x+y=26. As there are 26 of each color in the deck, then x+?=26 for the black cards in the deck and ?+y=26 for the red cards in the deck. As x+y=26 in the first randomly selected 26 cards, then the value of black cards in the other half of the deck must equal y, and the value of red cards in the other half of the deck must equal x meaning that "there will always be as many red cards in the first half of the deck as there are black cards in the second half of the deck."

==16. Suppose that each daughter in your family has the same number of brothers as she has sisters, and each son in your family has twice as many sisters as he has brothers. How many sons and daughters are in the family?==

Answer:3 total, 2 sister and 1 brother
Solution: Since the daughters in the family each have as many brothers as sisters the amount of sisters, with x standing for the amount of brothers, is x+1. As each brother has twice as many sisters as brothers, the amount of sisters must equal 2(x-1) or 2x-2. To find the number of brother: x+1=2x+1, 1=x-2, 3=x, which means that their are 3 brothers and 4 sisters (x+1= the number of sisters and x=3). This makes sense because a sister would have an equal amount of brothers to sisters, 3 sisters and 3 brothers, if there were 4 sisters and 3 brothers total, and each brother would have 4 sisters and 3 brothers, which is twice the amount of brothers to sisters.

==17~21==
==Audrey Chen==

==17.The zero point on a bathroom scale is set incorrectly, but otherwise the scale is accurate. It shows 60 kg when Dan stands on the scale, 50 kg when Sarah stands on the scale, but 105 kg when Dan and Sarah both stand on the scale. Does the scale read too high or too low? Explain. ==

''The scale read too low, since Dan is shown as 60kg and Sarah is 50kg, suppose 60+50=110, 105-110=-5, so that means the scale is smaller than 0 in the beginning''

==18. Alice takes one-third of the pennies from a large jar. Then Bret takes one-third of the remaining pennies from the jar. Finally, Carla takes one-third of the remaining pennies from the jar, leaving 40 pennies in the jar. How many pennies were in the jar at the start? ==

''If the total pennies is "x", Alice take 1/3x, so it has 2/3x left after Alice took it, than Bret take 1/3 out, after Alice took it, which is 2/3x*1/3= 2/9x, so in the beginning they have x, after Alice took it, it has 2/3x left, and Bret took 2/9x, so after Bret took it, it becomes 2/3x-2/9x= 4/9x-2/9x=2/9x left in the jar. Than Carla take 1/3 of the rest, so she took 1/3 of rest which is 2/9x*1/3=3/27x, so Alice took 1/3x, Bret tool 2/9x, Carla took 3/27x, three of them totaly took 1/3x+2/9x+3/27x=18/27x, so there still has x-18/27x= 9/27x= 1/3 left, 1/3x=40pennies, so x=120 pennies, so it was having 120 pennies in the jar.

==19. One morning each member of Angela's family drank an eight-ounce cup of coffee and milk, with the (nonzero) amounts of coffee and milk varying from cup to cup. Angela drank a quarter of the total amount of milk and a sixth of the total amount of coffee. What is the least number of people in the family? ==

''If we let total milk is x, total coffee is y. Than 1/4x+1/6y=8, and because every cup is 8ounce, x+y is multiple by 8. So make it easier, we use 1/4x+1/6y=8 * 12 to both sides. than we will got 3x+2y=96, now we have 3x+2y=96 and x+y is multiple of 8, and the number that multiple by 8 is 8, 16, 24, 32... so 2x+2y= 16, 32, 48, 64, 80, 96, since 3x+2y=96, it can't be more than 96. It will only have 6 possible number, so if you take 3x+2y=96 substracting 2x+2y=16, 32, 48, 64, 80, 96 you can get 6 possible x, which are 80, 64, 48, 32, 16, and 0. Than put the number into 3x+2y=96, if you put 80 in, will get 20, which is bigger than 8, and also 64, 48. If we use 32, it will equal to 8, but that means we have 0 coffee, but coffee can't be 0, so there's only 16 and 0 left. Since Angela had 1/4 of total amount of milk, milk can't be 0. So we got 16ounce than 16*(1/4)=4, so that means she had 8-4=4 's coffee. So 4=1/6 coffee, than the total amount of coffee would be 4*6=24. than x=16 and y=24, 16+24=40 40/8ounce=5, so at least have 5 cups of drinks, so that means at least they have 5 members in Angela's family.''

==20.Of two clocks next to each other, one runs 5 min per hour fast and the other runs 5 min per hour slow. At midnight the clocks show the same time. At what time are they are one hour apart? ==

''Since one clock runs 5 min faster per hour, the other is 5 min slower, after clock runs an hour, two clocks will have 10 min different from each other. 60 min an hour. 60/10=6, so after 6 hours two clocks will having one hour apart, and that would be 6AM.''

==21.Sven placed exactly in the middle among all runners in a race. Dan was slower than Sven, in 10th place, and Lars was in 16th place. How many runners were in the race? ==

''There were 17 runners. Since lars was in 16th place, the runners at least have to be 16, than if Sven is placed exactly in the middle, it means it would have even number of runners. Because Dan is slower and he was at 10 place that tells us Seven has to be before 10th, and if there has 19 runners, Sven and Dan would be at the same place, so it should be 17 runners, than Sven would be at exactly in the middle which at 9th place.''

==22-25==

==Roland Will==

==22. During a vacation, it rained on 13 days, but when it rained in the morning, the afternoon was sunny, and every rainy afternoon was preceded by a sunny morning. There were 11 sunny mornings and 12 sunny afternoons. How long was the vacation?==

Answer: 18 days of vacation.

Solution: 13 of the days of vacation were half sunny and half rainy. As there were 23 sunny mornings and afternoons (11 sunny mornings+12 sunny afternoons = 23 sunny mornings and afternoons), 13 of those sunny afternoons or mornings were on half rainy days. This means there are 10 sunny half-days left over, which equal 5 sunny full days. The 5 sunny full days plus the 13 half sunny/rainy days equal 18 total days of vacation.

==23. Suppose you overhear the following conversation: Paul: How old are your three children? Paula: The product of their ages is 36 and the sum of their ages is the same as today's date. Paul: That is not enough information. Paula: The oldest child also has red hair. If you were Paul could you determine the ages of Paula's children? Explain.==

Answer: If I were Paul this might be possible, but since we don’t know the date that Paula said this, it is not possible for us to find out.

Solution: There are many different combinations of three numbers that can be multiplied and will produce 36. As we do not know the date that Paula said this, the only thing we can be sure of is that the sum of the ages is less than 31 because no month has more than 31 days. Unfortunately, only one set of ages (ages 1 year old, 1 year old and 36 years old) has a sum greater than 31, which leaves many possible combinations open as possible. For today’s date, the 13th, ages of 2, 2, and 9 would produce 36 and have a sum of 13, but, again, it is uncertain. If it were the first of the month, there would be no possible combinations that would produce 36 and sum 1.

==24. Two candles of equal length were lit at the same time. One candle took 6 hr to burn out and the other candle took 3 hr to burn out. After how much time was one candle exactly twice as long as the other candle?==

Answer: 2 hours.

Solution: The faster burning candle took half the time to burn as the slower burning candle (3 hours/ 6 hours = 1/2), meaning it burned twice as fast. This means that after 2/3 of the total burning time for the faster burning candle it will be 1/3 of its original height and at the slower burning candle will be at 2/3 of its original height and 1/3 is half of 2/3. Since the faster burning candle took 3 hours to burn, 2/3 of its total burning time is 2 hours.

==25. Two candles of length L and L + 1 were lit at 6:00 and 4:30, respectively. At 8:30 they had the same length. The longer candle died at 10:30 and the shorter candle died at 10:00. Find L.==

Answer: L=2.

Solution: The shorter candle lasted for 4 hours and the longer candle lasted for 6 hours. As 6 hours – 4 hours = 2 hours and 2 hours / 4 hours = 1/2, the longer candle lasted 50% longer and was, therefore, 50% longer in length. This means that the +1 in L+1 on the longer candle was 1/2 of L. 1/2L=1, so L=2*1, L=2.

Course:MATH110/Archive/2010-2011/003/Groups/Group 18/Homework October 20th, 2010

2010-10-20T06:18:36Z

RolandWill: My (Roland Will's) contribution to the group homework due on the 20th of October 2010

==MATH110/003/Groups/Group18HomeworkOctober20th,2010==

==Roland Will==

Adam, Bobo, Charles, Ed, Hassan, Jason, Mathieu, Pascal and Sung have formed a baseball team. The following facts are true:

* Adam does not like the catcher,
* Ed's sister is engaged to the second baseman,
* The centre fielder is taller than the right fielder,
* Hassan and the third baseman live in the same building,
* Pascal and Charles each won $20 from the pitcher at a poker game,
* Ed and the outfielders play cards during their free time,
* The pitcher's wife is the third baseman's sister,
* All the battery and infield except Charles, Hassan and Adam are shorter than Sung,
* Pascal, Adam and the shortstop lost $100 each at the race track,
* The second baseman beat Pascal, Hassan, Bobo and the catcher at billiards,
* Sung is in the process of getting a divorce,
* The catcher and the third baseman each have two legitimate children,
* Ed, Pascal Jason, the right fielder and the centre fielder are bachelors, the others are all married
* The shortstop, the third baseman and Bobo all attended the fight,
* Mathieu is the shortest player of the team,

Determine the positions of each player on the baseball team.

Note: On a baseball team there are three outfielders (right, centre and left), four infielders (first baseman, second baseman, third baseman and shortstop) and the battery (pitcher and catcher).

Course:MATH110/Archive/2010-2011/003/Groups/Group 18

2010-10-13T10:48:54Z

RolandWill:

Group members:
* Audrey Chen
* Sifat Hasan
* Caitlin Lastiwka-Farquharson
* Victoria Wall
* Roland Will
==1-5==
==Victoria Wall ==
==1.A bus traveled from the terminal to the airport at an average speed of 30 mi/hr and the trip took an hour and 20 min. The bus then traveled from the airport back to the terminal and again averaged 30 mi/hr. However, the return trip required 80 min. Explain.==

' 'Lets call the terminal T and the airport A. If the bus travelled from T to A at 30mi/hr and it took them one hour and 20 mins to get from T to A at this speed, and there are 60 minutes in one hour, it took the bus 60min + 20min to get to A which is a total of 80min. The bus took 80 min to get from T to A. To get from A to T at the same speed (30mi/hr) it took the bus 80min. 80min = 80 min. This means going from A to T or vis versa at 30 mi/hr it will take the bus 80min.

==2.A lady did not have her driver's license with her when she failed to stop at a stop sign and then went three blocks down a one-way street the wrong way. A policeman saw her, but he did not stop her. Explain. ==

' 'The lady was walking. It never says she was driving.

==3.One of three boxes contains apples, another box contains oranges, and another box contains a mixture of apples and oranges. The boxes are labeled APPLES, ORANGES and APPLES AND ORANGES, but each label is incorrect. Can you select one fruit from only one box and determine the correct labels? Explain. ==

' 'if you selecet from the box APPLES AND ORANGES then you will be able to see the labels if they are correct or not.

==4.I am the brother of the blind fiddler, but brothers I have none. How can this be? ==

' 'Since it says that he is the brother of the blind fiddler it does not mean that the fiddle is male, since he has no brothers than the fiddler must be a female.

==5.Two quarters rest next to each other on a table. One coin is held fixed while the second coin is rolled around the edge of the first coin with no slipping. When the moving coin returns to its original position, how many times has it revolved? ==

' 'This is because the moving quarters revolves two full revolutions

==6-10==
== Caitlin Lastiwka- Farquharson ==

==6. Three kinds of apples are all mixed up in a basket. How many apples must you draw without (without looking) from the basket to be sure of getting at least two of a kind? ==

' ' To be sure you are getting at least two of a kind, you must select all of the other types of apples, plus two more. Meaning that only once you have selected all of the other apples can you be sure that you will select two of the kind you desire. It can be written like this: x,a x2, b and x3, c, with x representing the quantity of apples. This can be calculated by x2 + x3 +2. X2 representing one of the types of apples, x3 representing the other type and 2 representing 2 of the kind of apples you are trying to select. This is the only way to be sure you are getting at least two of a kind. ' '

==7. Suppose you have 40 blue socks and 40 brown socks in a drawer. How many socks must you take from the drawer (without looking) to be sure of getting (i) a pair of the same colour, and (ii) a pair with different colors. ==

' 'You must take three socks from the drawer to ensure you have a pair that match. This is because if you only select two, one could be brown and one could be blue. Selecting three, ensures that at least two of them will be the same colour. As for part two, you would need to select 41 socks to ensure you had a pair of different coloured socks because if you select 40 or less you could get all the same colour, but selecting 41 ensures you will have at least one pair of mixed colour. ' '

==8. Rueben says "Two days ago I was 20 years old. Later next year I will be 23 years old." Explain how this is possible. ==

' 'It is possible if your birthday is on the 31st of December and today is the 1st of January. This is because on the 30th of December (two days ago) you we’re 20 years old and now you are 21, later this year you will turn 22 on the 31st of December, and therefore 23 the next year.' '

==9. A rope ladder hanging over the side of a boat has rungs one foot apart. Ten rungs are showing. If the tide rises five feet, how many rungs will be showing? ==

' ' 5 rungs will be showing, because if there are 10 showing now, and they are each a foot apart, then for 5 more rungs to be showing there would need to be an increase in the level of water by 5 feet. ' '

==10.Suppose one-half of all people are chocolate eaters and one-half of all people are women. (i) Does it follow that one-fourth of all people are women chocolate eaters? (ii) Does it follow that one-half of all men are chocolate eaters? Explain. ==

' ' No, it does not follow that one-fourth of all people are women chocolate eaters and it does not follow that half of all men are chocolate eaters because are completely independent scenarios. Meaning that the the amount of women there are does not influence the amount of men that will eat chocolate. For example, If 50% of people are women and 50% of the entire population including men and women eat chocolate (arrived at by using the same logic that if 1/4 of women eat chocolate and 1/4 of men eat chocolate), that entire 50% could be comprised of women, meaning that no men eat chocolate disproving the statement.

==15-16==
==Roland Will==

==15. Alex says to you, “I'll bet you any amount of money that if I shuffle this deck of cards, there will always be as many red cards in the first half of the deck as there are black cards in the second half of the deck.” Should you accept his bet?==

Answer: No, you shouldn't assuming the deck has equal amounts of red and black cards as in a standard 52 card deck.
Solution: In a standard 52 card deck, half of the cards (26) are black and half are red. If you take 26 cards at random from the deck, x of them will be black and y of them will be red, and x+y=26. As there are 26 of each color in the deck, then x+?=26 for the black cards in the deck and ?+y=26 for the red cards in the deck. As x+y=26 in the first randomly selected 26 cards, then the value of black cards in the other half of the deck must equal y, and the value of red cards in the other half of the deck must equal x meaning that "there will always be as many red cards in the first half of the deck as there are black cards in the second half of the deck."

==16. Suppose that each daughter in your family has the same number of brothers as she has sisters, and each son in your family has twice as many sisters as he has brothers. How many sons and daughters are in the family?==

Answer:3 total, 2 sister and 1 brother
Solution: Since the daughters in the family each have as many brothers as sisters the amount of sisters, with x standing for the amount of brothers, is x+1. As each brother has twice as many sisters as brothers, the amount of sisters must equal 2(x-1) or 2x-2. To find the number of brother: x+1=2x+1, 1=x-2, 3=x, which means that their are 3 brothers and 4 sisters (x+1= the number of sisters and x=3). This makes sense because a sister would have an equal amount of brothers to sisters, 3 sisters and 3 brothers, if there were 4 sisters and 3 brothers total, and each brother would have 4 sisters and 3 brothers, which is twice the amount of brothers to sisters.

==17~21==
==Audrey Chen==

==17.The zero point on a bathroom scale is set incorrectly, but otherwise the scale is accurate. It shows 60 kg when Dan stands on the scale, 50 kg when Sarah stands on the scale, but 105 kg when Dan and Sarah both stand on the scale. Does the scale read too high or too low? Explain. ==

''The scale read too low, since Dan is shown as 60kg and Sarah is 50kg, suppose 60+50=110, 105-110=-5, so that means the scale is smaller than 0 in the beginning''

==18. Alice takes one-third of the pennies from a large jar. Then Bret takes one-third of the remaining pennies from the jar. Finally, Carla takes one-third of the remaining pennies from the jar, leaving 40 pennies in the jar. How many pennies were in the jar at the start? ==

''If the total pennies is "x", Alice take 1/3x, so it has 2/3x left after Alice took it, than Bret take 1/3 out, after Alice took it, which is 2/3x*1/3= 2/9x, so in the beginning they have x, after Alice took it, it has 2/3x left, and Bret took 2/9x, so after Bret took it, it becomes 2/3x-2/9x= 4/9x-2/9x=2/9x left in the jar. Than Carla take 1/3 of the rest, so she took 1/3 of rest which is 2/9x*1/3=3/27x, so Alice took 1/3x, Bret tool 2/9x, Carla took 3/27x, three of them totaly took 1/3x+2/9x+3/27x=18/27x, so there still has x-18/27x= 9/27x= 1/3 left, 1/3x=40pennies, so x=120 pennies, so it was having 120 pennies in the jar.

==19. One morning each member of Angela's family drank an eight-ounce cup of coffee and milk, with the (nonzero) amounts of coffee and milk varying from cup to cup. Angela drank a quarter of the total amount of milk and a sixth of the total amount of coffee. What is the least number of people in the family? ==

''If we let total milk is x, total coffee is y. Than 1/4x+1/6y=8, and because every cup is 8ounce, x+y is multiple by 8. So make it easier, we use 1/4x+1/6y=8 * 12 to both sides. than we will got 3x+2y=96, now we have 3x+2y=96 and x+y is multiple of 8, and the number that multiple by 8 is 8, 16, 24, 32... so 2x+2y= 16, 32, 48, 64, 80, 96, since 3x+2y=96, it can't be more than 96. It will only have 6 possible number, so if you take 3x+2y=96 substracting 2x+2y=16, 32, 48, 64, 80, 96 you can get 6 possible x, which are 80, 64, 48, 32, 16, and 0. Than put the number into 3x+2y=96, if you put 80 in, will get 20, which is bigger than 8, and also 64, 48. If we use 32, it will equal to 8, but that means we have 0 coffee, but coffee can't be 0, so there's only 16 and 0 left. Since Angela had 1/4 of total amount of milk, milk can't be 0. So we got 16ounce than 16*(1/4)=4, so that means she had 8-4=4 's coffee. So 4=1/6 coffee, than the total amount of coffee would be 4*6=24. than x=16 and y=24, 16+24=40 40/8ounce=5, so at least have 5 cups of drinks, so that means at least they have 5 members in Angela's family.''

==20.Of two clocks next to each other, one runs 5 min per hour fast and the other runs 5 min per hour slow. At midnight the clocks show the same time. At what time are they are one hour apart? ==

''Since one clock runs 5 min faster per hour, the other is 5 min slower, after clock runs an hour, two clocks will have 10 min different from each other. 60 min an hour. 60/10=6, so after 6 hours two clocks will having one hour apart, and that would be 6AM.''

==21.Sven placed exactly in the middle among all runners in a race. Dan was slower than Sven, in 10th place, and Lars was in 16th place. How many runners were in the race? ==

''There were 17 runners. Since lars was in 16th place, the runners at least have to be 16, than if Sven is placed exactly in the middle, it means it would have even number of runners. Because Dan is slower and he was at 10 place that tells us Seven has to be before 10th, and if there has 19 runners, Sven and Dan would be at the same place, so it should be 17 runners, than Sven would be at exactly in the middle which at 9th place.''

==22-25==

==Roland Will==

==22. During a vacation, it rained on 13 days, but when it rained in the morning, the afternoon was sunny, and every rainy afternoon was preceded by a sunny morning. There were 11 sunny mornings and 12 sunny afternoons. How long was the vacation?==

Answer: 18 days of vacation.

Solution: 13 of the days of vacation were half sunny and half rainy. As there were 23 sunny mornings and afternoons (11 sunny mornings+12 sunny afternoons = 23 sunny mornings and afternoons), 13 of those sunny afternoons or mornings were on half rainy days. This means there are 10 sunny half-days left over, which equal 5 sunny full days. The 5 sunny full days plus the 13 half sunny/rainy days equal 18 total days of vacation.

==23. Suppose you overhear the following conversation: Paul: How old are your three children? Paula: The product of their ages is 36 and the sum of their ages is the same as today's date. Paul: That is not enough information. Paula: The oldest child also has red hair. If you were Paul could you determine the ages of Paula's children? Explain.==

Answer: If I were Paul this might be possible, but since we don’t know the date that Paula said this, it is not possible for us to find out.

Solution: There are many different combinations of three numbers that can be multiplied and will produce 36. As we do not know the date that Paula said this, the only thing we can be sure of is that the sum of the ages is less than 31 because no month has more than 31 days. Unfortunately, only one set of ages (ages 1 year old, 1 year old and 36 years old) has a sum greater than 31, which leaves many possible combinations open as possible. For today’s date, the 13th, ages of 2, 2, and 9 would produce 36 and have a sum of 13, but, again, it is uncertain. If it were the first of the month, there would be no possible combinations that would produce 36 and sum 1.

==24. Two candles of equal length were lit at the same time. One candle took 6 hr to burn out and the other candle took 3 hr to burn out. After how much time was one candle exactly twice as long as the other candle?==

Answer: 2 hours.

Solution: The faster burning candle took half the time to burn as the slower burning candle (3 hours/ 6 hours = 1/2), meaning it burned twice as fast. This means that after 2/3 of the total burning time for the faster burning candle it will be 1/3 of its original height and at the slower burning candle will be at 2/3 of its original height and 1/3 is half of 2/3. Since the faster burning candle took 3 hours to burn, 2/3 of its total burning time is 2 hours.

==25. Two candles of length L and L + 1 were lit at 6:00 and 4:30, respectively. At 8:30 they had the same length. The longer candle died at 10:30 and the shorter candle died at 10:00. Find L.==

Answer: L=2.

Solution: The shorter candle lasted for 4 hours and the longer candle lasted for 6 hours. As 6 hours – 4 hours = 2 hours and 2 hours / 4 hours = 1/2, the longer candle lasted 50% longer and was, therefore, 50% longer in length. This means that the +1 in L+1 on the longer candle was 1/2 of L. 1/2L=1, so L=2*1, L=2.

Course:MATH110/Archive/2010-2011/003/Groups/Group 18

2010-10-13T09:30:17Z

RolandWill:

Group members:
* Audrey Chen
* Sifat Hasan
* Caitlin Lastiwka-Farquharson
* Victoria Wall
* Roland Will
==1-5==
==Victoria Wall ==
==1.A bus traveled from the terminal to the airport at an average speed of 30 mi/hr and the trip took an hour and 20 min. The bus then traveled from the airport back to the terminal and again averaged 30 mi/hr. However, the return trip required 80 min. Explain.==

' 'Lets call the terminal T and the airport A. If the bus travelled from T to A at 30mi/hr and it took them one hour and 20 mins to get from T to A at this speed, and there are 60 minutes in one hour, it took the bus 60min + 20min to get to A which is a total of 80min. The bus took 80 min to get from T to A. To get from A to T at the same speed (30mi/hr) it took the bus 80min. 80min = 80 min. This means going from A to T or vis versa at 30 mi/hr it will take the bus 80min.

==2.A lady did not have her driver's license with her when she failed to stop at a stop sign and then went three blocks down a one-way street the wrong way. A policeman saw her, but he did not stop her. Explain. ==

' 'The lady was walking. It never says she was driving.

==3.One of three boxes contains apples, another box contains oranges, and another box contains a mixture of apples and oranges. The boxes are labeled APPLES, ORANGES and APPLES AND ORANGES, but each label is incorrect. Can you select one fruit from only one box and determine the correct labels? Explain. ==

' 'if you selecet from the box APPLES AND ORANGES then you will be able to see the labels if they are correct or not.

==4.I am the brother of the blind fiddler, but brothers I have none. How can this be? ==

' 'Since it says that he is the brother of the blind fiddler it does not mean that the fiddle is male, since he has no brothers than the fiddler must be a female.

==5.Two quarters rest next to each other on a table. One coin is held fixed while the second coin is rolled around the edge of the first coin with no slipping. When the moving coin returns to its original position, how many times has it revolved? ==

' 'This is because the moving quarters revolves two full revolutions

==6-10==
== Caitlin Lastiwka- Farquharson ==

==6. Three kinds of apples are all mixed up in a basket. How many apples must you draw without (without looking) from the basket to be sure of getting at least two of a kind? ==

' ' To be sure you are getting at least two of a kind, you must select all of the other types of apples, plus two more. Meaning that only once you have selected all of the other apples can you be sure that you will select two of the kind you desire. It can be written like this: x,a x2, b and x3, c, with x representing the quantity of apples. This can be calculated by x2 + x3 +2. X2 representing one of the types of apples, x3 representing the other type and 2 representing 2 of the kind of apples you are trying to select. This is the only way to be sure you are getting at least two of a kind. ' '

==7. Suppose you have 40 blue socks and 40 brown socks in a drawer. How many socks must you take from the drawer (without looking) to be sure of getting (i) a pair of the same colour, and (ii) a pair with different colors. ==

' 'You must take three socks from the drawer to ensure you have a pair that match. This is because if you only select two, one could be brown and one could be blue. Selecting three, ensures that at least two of them will be the same colour. As for part two, you would need to select 41 socks to ensure you had a pair of different coloured socks because if you select 40 or less you could get all the same colour, but selecting 41 ensures you will have at least one pair of mixed colour. ' '

==8. Rueben says "Two days ago I was 20 years old. Later next year I will be 23 years old." Explain how this is possible. ==

' 'It is possible if your birthday is on the 31st of December and today is the 1st of January. This is because on the 30th of December (two days ago) you we’re 20 years old and now you are 21, later this year you will turn 22 on the 31st of December, and therefore 23 the next year.' '

==9. A rope ladder hanging over the side of a boat has rungs one foot apart. Ten rungs are showing. If the tide rises five feet, how many rungs will be showing? ==

' ' 5 rungs will be showing, because if there are 10 showing now, and they are each a foot apart, then for 5 more rungs to be showing there would need to be an increase in the level of water by 5 feet. ' '

==10.Suppose one-half of all people are chocolate eaters and one-half of all people are women. (i) Does it follow that one-fourth of all people are women chocolate eaters? (ii) Does it follow that one-half of all men are chocolate eaters? Explain. ==

' ' No, it does not follow that one-fourth of all people are women chocolate eaters and it does not follow that half of all men are chocolate eaters because are completely independent scenarios. Meaning that the the amount of women there are does not influence the amount of men that will eat chocolate. For example, If 50% of people are women and 50% of the entire population including men and women eat chocolate (arrived at by using the same logic that if 1/4 of women eat chocolate and 1/4 of men eat chocolate), that entire 50% could be comprised of women, meaning that no men eat chocolate disproving the statement.

==17~21==
==Audrey Chen==

==17.The zero point on a bathroom scale is set incorrectly, but otherwise the scale is accurate. It shows 60 kg when Dan stands on the scale, 50 kg when Sarah stands on the scale, but 105 kg when Dan and Sarah both stand on the scale. Does the scale read too high or too low? Explain. ==

''The scale read too low, since Dan is shown as 60kg and Sarah is 50kg, suppose 60+50=110, 105-110=-5, so that means the scale is smaller than 0 in the beginning''

==18. Alice takes one-third of the pennies from a large jar. Then Bret takes one-third of the remaining pennies from the jar. Finally, Carla takes one-third of the remaining pennies from the jar, leaving 40 pennies in the jar. How many pennies were in the jar at the start? ==

''If the total pennies is "x", Alice take 1/3x, so it has 2/3x left after Alice took it, than Bret take 1/3 out, after Alice took it, which is 2/3x*1/3= 2/9x, so in the beginning they have x, after Alice took it, it has 2/3x left, and Bret took 2/9x, so after Bret took it, it becomes 2/3x-2/9x= 4/9x-2/9x=2/9x left in the jar. Than Carla take 1/3 of the rest, so she took 1/3 of rest which is 2/9x*1/3=3/27x, so Alice took 1/3x, Bret tool 2/9x, Carla took 3/27x, three of them totaly took 1/3x+2/9x+3/27x=18/27x, so there still has x-18/27x= 9/27x= 1/3 left, 1/3x=40pennies, so x=120 pennies, so it was having 120 pennies in the jar.

==19. One morning each member of Angela's family drank an eight-ounce cup of coffee and milk, with the (nonzero) amounts of coffee and milk varying from cup to cup. Angela drank a quarter of the total amount of milk and a sixth of the total amount of coffee. What is the least number of people in the family? ==

''If we let total milk is x, total coffee is y. Than 1/4x+1/6y=8, and because every cup is 8ounce, x+y is multiple by 8. So make it easier, we use 1/4x+1/6y=8 * 12 to both sides. than we will got 3x+2y=96, now we have 3x+2y=96 and x+y is multiple of 8, and the number that multiple by 8 is 8, 16, 24, 32... so 2x+2y= 16, 32, 48, 64, 80, 96, since 3x+2y=96, it can't be more than 96. It will only have 6 possible number, so if you take 3x+2y=96 substracting 2x+2y=16, 32, 48, 64, 80, 96 you can get 6 possible x, which are 80, 64, 48, 32, 16, and 0. Than put the number into 3x+2y=96, if you put 80 in, will get 20, which is bigger than 8, and also 64, 48. If we use 32, it will equal to 8, but that means we have 0 coffee, but coffee can't be 0, so there's only 16 and 0 left. Since Angela had 1/4 of total amount of milk, milk can't be 0. So we got 16ounce than 16*(1/4)=4, so that means she had 8-4=4 's coffee. So 4=1/6 coffee, than the total amount of coffee would be 4*6=24. than x=16 and y=24, 16+24=40 40/8ounce=5, so at least have 5 cups of drinks, so that means at least they have 5 members in Angela's family.''

==20.Of two clocks next to each other, one runs 5 min per hour fast and the other runs 5 min per hour slow. At midnight the clocks show the same time. At what time are they are one hour apart? ==

''Since one clock runs 5 min faster per hour, the other is 5 min slower, after clock runs an hour, two clocks will have 10 min different from each other. 60 min an hour. 60/10=6, so after 6 hours two clocks will having one hour apart, and that would be 6AM.''

==21.Sven placed exactly in the middle among all runners in a race. Dan was slower than Sven, in 10th place, and Lars was in 16th place. How many runners were in the race? ==

''There were 17 runners. Since lars was in 16th place, the runners at least have to be 16, than if Sven is placed exactly in the middle, it means it would have even number of runners. Because Dan is slower and he was at 10 place that tells us Seven has to be before 10th, and if there has 19 runners, Sven and Dan would be at the same place, so it should be 17 runners, than Sven would be at exactly in the middle which at 9th place.''

==22-25==

==Roland Will==

==22. During a vacation, it rained on 13 days, but when it rained in the morning, the afternoon was sunny, and every rainy afternoon was preceded by a sunny morning. There were 11 sunny mornings and 12 sunny afternoons. How long was the vacation?==

Answer: 18 days of vacation.

Solution: 13 of the days of vacation were half sunny and half rainy. As there were 23 sunny mornings and afternoons (11 sunny mornings+12 sunny afternoons = 23 sunny mornings and afternoons), 13 of those sunny afternoons or mornings were on half rainy days. This means there are 10 sunny half-days left over, which equal 5 sunny full days. The 5 sunny full days plus the 13 half sunny/rainy days equal 18 total days of vacation.

==23. Suppose you overhear the following conversation: Paul: How old are your three children? Paula: The product of their ages is 36 and the sum of their ages is the same as today's date. Paul: That is not enough information. Paula: The oldest child also has red hair. If you were Paul could you determine the ages of Paula's children? Explain.==

Answer: If I were Paul this might be possible, but since we don’t know the date that Paula said this, it is not possible for us to find out.

Solution: There are many different combinations of three numbers that can be multiplied and will produce 36. As we do not know the date that Paula said this, the only thing we can be sure of is that the sum of the ages is less than 31 because no month has more than 31 days. Unfortunately, only one set of ages (ages 1 year old, 1 year old and 36 years old) has a sum greater than 31, which leaves many possible combinations open as possible. For today’s date, the 13th, ages of 2, 2, and 9 would produce 36 and have a sum of 13, but, again, it is uncertain. If it were the first of the month, there would be no possible combinations that would produce 36 and sum 1.

==24. Two candles of equal length were lit at the same time. One candle took 6 hr to burn out and the other candle took 3 hr to burn out. After how much time was one candle exactly twice as long as the other candle?==

Answer: 2 hours.

Solution: The faster burning candle took half the time to burn as the slower burning candle (3 hours/ 6 hours = 1/2), meaning it burned twice as fast. This means that after 2/3 of the total burning time for the faster burning candle it will be 1/3 of its original height and at the slower burning candle will be at 2/3 of its original height and 1/3 is half of 2/3. Since the faster burning candle took 3 hours to burn, 2/3 of its total burning time is 2 hours.

==25. Two candles of length L and L + 1 were lit at 6:00 and 4:30, respectively. At 8:30 they had the same length. The longer candle died at 10:30 and the shorter candle died at 10:00. Find L.==

Answer: L=2.

Solution: The shorter candle lasted for 4 hours and the longer candle lasted for 6 hours. As 6 hours – 4 hours = 2 hours and 2 hours / 4 hours = 1/2, the longer candle lasted 50% longer and was, therefore, 50% longer in length. This means that the +1 in L+1 on the longer candle was 1/2 of L. 1/2L=1, so L=2*1, L=2.