Question

Ellie and Morgan go to the movie theater and purchase refreshments for their friends. Ellie spends a total of $36.50 on 7 bags of popcorn and 2 drinks. Morgan spends a total of $155.50 on 9 bags of popcorn and 14 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 bag of popcorn, to the nearest cent.

Answer 1

Ellie:
Total spending = $36.50
Number of popcorn bags bought = 7
Number of drinks bought = 2

Morgan:
Total spending = $155.50
Number of popcorn bags bought = 9
Number of drinks bought = 14

Part 1:
If
P = Price of one popcorn bag
D = Price of one drink
Then,
For Ellie: 7P + 2D = 36.50
For Morgan: 9P + 14 D = 155.50

Set of equations:
7P + 2D = 36.5 --------(1)
9P + 14D = 155.5 ---- (2)

Part 2:
Solving equations (1) and (2)
Multiply (1) by 7 and subtract (2) from resulting equation;
49P + 14D = 255.5
9P + 14D = 155.5
-------------------------
40P = 100
P = 100/40 = 2.5

From eqn (1),
7*2.5 + 2D = 36.5
17.5 +2D = 36.5
2D = 19
D = 19/2 = 9.5

Therefore,
Bag of popcorn costs $2.50