Delta Math - Linear System Word Problem - Movie

Question

Sophie and Elizabeth go to the movie theater and purchase refreshments for their friends.

Sophie spends a total of $72.50 on 5 drinks and 5 bags of popcorn.

Elizabeth spends a total of $163.50 on 15 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 drink, to the nearest cent.

Answer 1

d=price of drinks

p=price of popcorn

First write two equations from the given information.

5d+5p=72.50

15d+3p=163.50

Solve by elimination. Multiply the first equation times -3

-3(5d+5p=72.50) This equals

-15d-15p=-217.50 Then add the second equation

15d+3p=163.50 This equals

-12p=-54 Divide both sides by -12

-12p/-12=-54/-12

p=4.50. The popcorn cost $4.50. Substitute to find d

5d +5(4.50)=72.50

5d+22.50=72.50 subtract 22.50 from both sides

5d+22.50-22.50=72.50-22.50

5d=50 Divide both sides by 5

5d/5=50/5

d=10

Drinks cost $10.00 each and popcorn costs $4.50 each.