Question

At the gas station, three small drinks and two large drinks contain 108 ounces of cola. A small drink contains a third as much cola as a large drink. How much cola does each size contain (I need to write an equation)

Answer 1

Small drink: 12 ounces

Large Drink: 36 ounces

Step-by-step 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

`3x+2y=108\rightarrow equation(1)`

b)A small drink contains a third as much cola as a large drink

`x=(1)/(3)y\rightarrow equation(2)`

Step 2

solve the equations

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

a) replace the x value from equation (2) into equation (1) and solve for y

`\begin{gathered} 3x+2y=108\rightarrow equation(1) \\ 3((1)/(3)y)+2y=108\rightarrow equation(1) \\ y+2y=108 \\ 3y=108 \\ \text{divide both sides by 3} \\ (3y)/(3)=(108)/(\cdot3) \\ y=36 \end{gathered}`

b) now, replace the y value into equaiton (2) to find the x value

`\begin{gathered} x=(1)/(3)y\rightarrow equation(2) \\ x=(1)/(3)36 \\ x=12 \end{gathered}`

therefore:

Small drink: 12 ounces

Large Drink: 36 ounces

I hope this helps you