SAT Question 340afb12: Systems of Linear Equations answer and explanation with Desmos solution

Choice C is correct. It’s given that Ellen bought two types of snack bags: chips and crackers. It’s also given that each box of chips contains $24$ bags. Thus, if Ellen bought $x$ boxes of chips, the number of bags of chips is $24x$. Additionally, it’s given that each box of chips costs $$11$. Thus, if Ellen bought $x$ boxes of chips, the cost for all the bags of chips is $11x$. It’s also given that each box of crackers contains $16$ bags. Thus, if Ellen bought $y$ boxes of crackers, the number of bags of crackers is $16y$. Additionally, it’s given that each box of crackers costs $$9$. Thus, if Ellen bought $y$ boxes of crackers, the cost for all the bags of crackers is $9y$. It’s given that it cost Ellen $$497$ to buy $968$ bags. Since Ellen bought $24x$ bags of chips and $16y$ bags of crackers, the total number of snack bags that Ellen bought can be represented by the equation $24x+16y=968$. Additionally, since the cost for all the bags of chips is $11x$ and the cost for all the bags of crackers is $9y$, the total cost for all the snack bags that Ellen bought can be represented by the equation $11x+9y=497$. Therefore, the system consisting of the equations $11x+9y=497$ and $24x+16y=968$ represents this situation.