Question

Emily and Lydia go to the movie theater and purchase refreshments for their friends. Emily spends a total of $78.50 on 2 bags of popcorn and 8 drinks. Lydia spends a total of $89.50 on 4 bags of popcorn and 7 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 drink, to the nearest cent.

Answer 1

The price of one drink is $7.5

The price of one bag of popcorn is $9.25

Explanation:

Let us assume,

• The price of one bag of popcorn = x
• The price of one drink = y

Emily spends a total of $78.50 on 2 bags of popcorn and 8 drinks.

⇒ 2x + 8y = 78.5 -------(1)

Lydia spends a total of $89.50 on 4 bags of popcorn and 7 drinks.

⇒ 4x + 7y = 89.5 --------(2)

To solve for x and y values :

Multiply eq (1) by 2 and subtract eq (2) from eq (1),

4x + 16y = 157

- (4x + 7y = 89.5)

9y = 67.5

⇒ y = 67.5/9

⇒ y = 7.5

∴ The price of one drink is $7.5

Substitute y = 7.5 in eq (1),

⇒ 2x + 8(7.5) = 78.5

⇒ 2x + 60 = 78.5

⇒ 2x = 78.5 - 60

⇒ 2x = 18.5

⇒ x = 18.5/2

⇒ x = 9.25

∴ The price of one bag of popcorn is $9.25