Answer :
Small drink: 12 ounces
Large Drink: 36 ounces
Explanation
Step 1
set the equations
let x represents the number of ounces of one small drink
let y represents the number of ounces of a large drink
hence
a)three small drinks and two large drinks contain 108 ounces of cola
[tex]3x+2y=108\rightarrow equation(1)[/tex]b)A small drink contains a third as much cola as a large drink
[tex]x=\frac{1}{3}y\rightarrow equation(2)[/tex]Step 2
solve the equations
[tex]\begin{gathered} 3x+2y=108\rightarrow equation(1) \\ x=\frac{1}{3}y\rightarrow equation(2) \end{gathered}[/tex]a) replace the x value from equation (2) into equation (1) and solve for y
[tex]\begin{gathered} 3x+2y=108\rightarrow equation(1) \\ 3(\frac{1}{3}y)+2y=108\rightarrow equation(1) \\ y+2y=108 \\ 3y=108 \\ \text{divide both sides by 3} \\ \frac{3y}{3}=\frac{108}{\cdot3} \\ y=36 \end{gathered}[/tex]b) now, replace the y value into equaiton (2) to find the x value
[tex]\begin{gathered} x=\frac{1}{3}y\rightarrow equation(2) \\ x=\frac{1}{3}36 \\ x=12 \end{gathered}[/tex]therefore:
Small drink: 12 ounces
Large Drink: 36 ounces
I hope this helps you