Question

2 (cups of cereal) and 1 (cup of milk) total 340 calories3 (cups of cereal) and 2 (cups of milk) total 570 caloriesHow many calories are in one cup of just cereal?

Answer 1

x = cereal

y = milk

then, we have the expressions

2x + y = 340 and 3x + 2y = 570

solve for x and y:

`\begin{gathered} \begin{bmatrix}2x+y=340 \\ 3x+2y=570\end{bmatrix} \\ x=(340-y)/(2) \\ 3\cdot(340-y)/(2)+2y=570 \\ (1020+y)/(2)=570 \\ (2\left(1020+y\right))/(2)=570\cdot\: 2 \\ 1020+y=1140 \\ 1020+y-1020=1140-1020 \\ y=120 \end{gathered}`

for x:

`\begin{gathered} x=(340-120)/(2) \\ x=(220)/(2) \\ x=110 \end{gathered}`

answer: 110 calories are in one cup of just cereal