Question

Three glasses of milk and 4 snack bars have a total of 80 carbohydrates (carbs), and 4 glasses of milk and 3 snack bars have a total of 81 carbs. Determine how many carbs are in one glass of milk and in one snack bar.

Answer 1

Let m be a glass of milk and s be a snack bar.

3 glasses of milk and 4 snack bars have a total of 80 carbohydrates. So, the expression is,

$3m+4s=80\ldots..(1)$

4 glasses of milk and 3 snack bars have a total of 81 carbs.

$4m+3s=81\ldots\ldots.(2)$

The above equation can be rewritten as,

$\begin{gathered} 4m=81-3s \\ m=\frac{81-3s}{4}\ldots..(3) \end{gathered}$

Put equ (3) in (1) to find s.

$\begin{gathered} 3\times(\frac{81-3s}{4})+4s=80 \\ \frac{243-9s}{4}+4s=80 \\ \frac{243-9s+16s}{4}=80 \\ 243-9s+16s=320 \\ 7s=77 \\ s=11 \end{gathered}$

Now, put 11 for s in equ (1) to find m.

$\begin{gathered} 3m+4\times11=80 \\ 3m+44=80 \\ 3m=36 \\ m=12 \end{gathered}$

So, there are