Question

Autumn and Kayla go to the movie theater and purchase refreshments for their friends. Autumn spends a total of $156.50 on 2 drinks and 15 bags of popcorn. Kayla spends a total of $59.25 on 3 drinks and 3 bags of popcorn. Write a system of equations that can be used to find the price of one drink and the price of one bag of popcorn. Using these equations, determine and state the price of a drink, to the nearest cent.

Answer 1

The price of one drink is $10.75

Explanation:

Let

$x = price of one drink

$y = price of popcorn.

Autumn:

Autumn spends a total of $156.50 on 2 drinks and 15 bags of popcorn.

Cost of 2 drinks = $2x

Cost of 15 popcorn = $15y

Total cost = $(2x+15y) = $156.50

Kayla:

Kayla spends a total of $59.25 on 3 drinks and 3 bags of popcorn.

Cost of 2 drinks = $3x

Cost of 15 popcorn = $3y

Total cost = $(3x+3y) = $59.25

You get the system of two equations:

`\left\{\begin{array}{l}2x+15y=156.50\\ \\3x+3x=59.25\end{array}\right.`

Divide the second equation by 3 and express y:

`x+y=19.75\\ \\y=19.75-x`

Substitute into the first equation:

`2x+15(19.75-x)=156.50\\ \\2x+296.25-15x=156.50\\ \\2x-15x=156.50-296.25\\ \\-13x=-139.75\\ \\13x=139.75\\ \\x=10.75\\ \\y=19.75-10.75=9`

The price of one drink is $10.75