Question

question 5
one month chang rented 6 movies and 2 video games for a total of $24. the next month he rented 3 movies and 5 video games for a total of $33. find the rental cost for each movie and each video game.
rental cost for each movie: $
rental cost for each video game: $

Explanation:

Step1: Define Variables

Let \( m \) be the cost of a movie (in dollars) and \( g \) be the cost of a video game (in dollars).

Step2: Set Up Equations

From the first month: \( 6m + 2g = 24 \).
From the next month: \( 3m + 5g = 33 \).
Simplify the first equation: Divide by 2: \( 3m + g = 12 \), so \( g = 12 - 3m \).

Step3: Substitute and Solve

Substitute \( g = 12 - 3m \) into the second equation:
\( 3m + 5(12 - 3m) = 33 \)
\( 3m + 60 - 15m = 33 \)
\( -12m = 33 - 60 \)
\( -12m = -27 \)
\( m = \frac{-27}{-12} = 2.25 \).

Step4: Find \( g \)

Substitute \( m = 2.25 \) into \( g = 12 - 3m \):
\( g = 12 - 3(2.25) = 12 - 6.75 = 5.25 \).

Answer:

Rental cost for each movie: $\boldsymbol{2.25}$
Rental cost for each video game: $\boldsymbol{5.25}$