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Gavin and Matthew go to the movie theater and purchase refreshments for their friends. Gavin spends a total of $15.50 on 3 drinks and 1 bag of popcorn. Matthew spends a total of $37.50 on 6 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 bag of popcorn, to the nearest cent.

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Answer:

Cost of a bag of popcorn is $6.5

A system of equations that can be used to find the price of one drink and the price of one bag of popcorn :

[tex]3x+y=15.50\\6x+3y=37.50[/tex]

Step-by-step explanation:

Let the cost of 1 drink be x and 1 bag of popcorn be y

So, cost of 3 drinks = 3x

Cost of 1 bag of popcorn = y

We are given that Gavin spends a total of $15.50 on 3 drinks and 1 bag of popcorn

So, 3x+y=15.50 ----1

We are also given that Matthew spends a total of $37.50 on 6 drinks and 3 bags of popcorn.

Cost of 6 drinks = 6x

Cost of 3 bags of popcorn = 3y

So,6x+3y=37.50 ----2

Substitute the values of y from 1 in 2

[tex]6x+3(15.50-3x)=37.50[/tex]

[tex]6x+46.5-9x=37.50[/tex]

[tex]46.5-37.50=3x[/tex]

[tex]\frac{46.5-37.50}{3}=x[/tex]

[tex]3=x[/tex]

Substitute the value of x in 1

[tex]3x+y=15.50[/tex]

[tex]3(3)+y=15.50[/tex]

[tex]y=15.50-9[/tex]

y=6.5

So, cost of 1 drink is $3

Cost of a bag of popcorn is $6.5

A system of equations that can be used to find the price of one drink and the price of one bag of popcorn :

[tex]3x+y=15.50\\6x+3y=37.50[/tex]

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