Question

Kylie and Amelia go to the movie theater and purchase refreshments for their friends. Kylie spends a total of $125.50 on 12 bags of popcorn and 7 drinks. Amelia spends a total of $87.50 on 6 bags of popcorn and 8 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

Answer: a drink costs $5.5

Step-by-step explanation:

Let x represent the cost of one bag of popcorn.

Let y represent the cost of one drink.

Kylie spends a total of $125.50 on 12 bags of popcorn and 7 drinks. This means that

12x + 7y = 125.50 - - - - - - - - - - 1

Amelia spends a total of $87.50 on 6 bags of popcorn and 8 drinks. This means that

6x + 8y = 87.50 - - - - - - - - - -- - - 2

Multiplying equation 1 by 1 and equation 2 by 2, it becomes

12x + 7y = 125.50

12x + 16y = 175

Subtracting, it becomes

- 9y = - 49.5

y = - 49.5/ - 9

y = 5.5

Substituting y = 5.5 into equation 2, it becomes

6x + 8 × 5.5 = 87.50

6x + 44 = 87.5

6x = 87.5 - 44 = 43.5

x = 43.5/6 = 7.25