Question

Kylie and Hailey go to the movie theater and purchase refreshments for their friends. Kylie spends a total of $52.50 on 5 bags of popcorn and 5 drinks. Hailey spends a total of $40.50 on 15 bags of popcorn and 2 drinks. Write a system of equations that can be used to find the price of one bag of popcorn and the price of one drink. Using these equations, determine and state the price of a bag of popcorn, to the nearest cent.

Answer 1

`5x+5y=52.50...(1)`

`15x+2y=40.50...(2)`

The price of a bag of popcorn = $1.50

Explanation:

Let x be the price of each bag of popcorn and y be the price of each drink.

We have been given that Kylie spends a total of $52.50 on 5 bags of popcorn and 5 drinks. This means that price of x bags of popcorn will be 5x and price of y drinks will be 5y.

We can represent this information in an equation as:

`5x+5y=52.50...(1)`

We are also told that Hailey spends a total of $40.50 on 15 bags of popcorn and 2 drinks. This means that price of x bags of popcorn will be 15x and price of y drinks will be 2y.

We can represent this information in an equation as:

`15x+2y=40.50...(2)`

Therefore, our desired system of equations will be:

`5x+5y=52.50...(1)`

`15x+2y=40.50...(2)`

Let us find price of one bag of popcorn using substitution method to solve system of equations.

From equation (1) we will get,

`y=(52.50-5x)/(5)`

Substituting this value in equation (2) we will get,

`15x+2((52.50-5x)/(5))=40.50`

`15x+(105-10x)/(5)=40.50`

Let us have a common denominator.

`(5*15x)/(5)+(105-10x)/(5)=40.50`

`(75x-10x+105)/(5)=40.50`

`(65x+105)/(5)=40.50`

Upon multiplying both sides of our equation by 5 we will get,

`5*(65x+105)/(5)=5*40.50`

`65x+105=202.50`

`65x+105-105=202.50-105`

`65x=97.50`

`(65x)/(65)=(97.50)/(65)`

`x=1.50`

Therefore, the price of one bag of popcorn is $1.50.