Question

2. At the gas station, three small drinks and two large drinks contain 108 ounces ofcola. A small drink contains a third as much cola as a large drink. How much coladoes each size drink contain?

Answer 1

Let x = small drinks

Let y = large drinks

3 small drinks and 2 large drinks contain 108 ounces of cola, this is:

3x + 2y = 108

A small drink contains a third as much cola as a large drink, this is:

x = 1/3y

Then, we solve the system of equations:

`\begin{gathered} 3x+2y=108 \\ x=(1)/(3)y \end{gathered}`

First, substitute x in equation 1:

`3((1)/(3)y)+2y=108`

And solve for y:

`\begin{gathered} y+2y=108 \\ 3y=108 \\ (3y)/(3)=(108)/(3) \\ y=36 \end{gathered}`

Next, substitute y = 36 in x:

`x=(1)/(3)y=(1)/(3)(36)=12`

Answer:

Small drinks: 12 ounces of cola

Large drinks: 36 ounces of cola