Science:Math Exam Resources/Courses/MATH152/April 2022/Question B1 (a)/Hint 2

Let $n_{A},\ n_{B},\ n_{C},\ n_{D}$ denote the numbers of boxes of each type of cookie that were produced. Then we have the following system of equations, where each row corresponds to the use of one of the ingredients:

$${\begin{cases}n_{A}+2n_{B}+n_{C}+3n_{D}&=11\\3n_{A}+6n_{B}+3n_{C}+9n_{D}&=33\\n_{A}+4n_{B}+3n_{C}+7n_{D}&=21\\2n_{A}+n_{B}+3n_{C}+8n_{D}&=23\\5n_{B}+n_{C}+2n_{D}&=H\end{cases}}.$$

Did you learn tools to reduce such a system to one that is as simple as possible?