Question

Sabrina and Raj go together to a local video store. Sabrina rents two movies and three games

for a total cost of $24.30. Raj rents three movies and one game for a total cost of $18.25. How
much does it cost to rent one movie? How much does it cost to rent one game?

Answer 1

• movie: $4.35
• game: $5.20

Explanation:

You want the cost of a movie rental and a game rental if 2 movies and 3 games rent for $24.30, while 3 movies and 1 game rent for $18.25.

Setup

The cost of rental can be summarized in the equations ...

• 2m +3g = 24.30
• 3m +1g = 18.25

Solution

Solving the second equation for g, we have ...

g = 18.25 -3m

Substituting that expression into the first equation gives ...

2m +3(18.25 -3m) = 24.30

-7m +54.75 = 24.30 . . . . . . . simplify

-7m = -30.45 . . . . . . . . . . . subtract 54.75

m = 4.35 . . . . . . . . . . . . divide by -7

g = 18.25 -3(4.35) = 5.20 . . . . find the cost of a game rental

It costs $4.35 to rent one movie; $5.20 to rent one game.