Question

Sophia and Sophie go to the movie theater and purchase refreshments for their friends. Sophia spends a total of $20.50 on 4 bags of popcorn and 2 drinks. Sophie spends a total of $34.50 on 6 bags of popcorn and 4 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

let the number of bags of popcorn = x

let the number of drinks = y

4x + 2y = 20.50 --- (1)

6x + 4y = 34.50 --- (2)

from (1) 4x + 2y = 20.50

2y = 20.50 - 4x

y = 10.25 - 2x --- (3)

substitute (3) into (2)

6x + 4y = 34.50

6x + 4(10.25-2x) = 34.50

6x + 41 - 8x = 34.50

-2x = 34.50 - 41

x = -6.5 / -2

x = 3.25 --- (4)

substitute (4) into (3)

y = 10.25 - 2x

y = 10.25 - 2(3.25)

y = 3.75

the price of one bag of popcorn = $3.25

the price of one drink = $3.75