Question

one month dante rented 4 movies and 8 video games for a total of $53. the next month he rented 2 movies and 3 video games for a total of $21. 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 rental cost of each movie (in dollars) and \( v \) be the rental cost of each video game (in dollars).

Step2: Set up equations

From the first month: \( 4m + 8v = 53 \)
From the second month: \( 2m + 3v = 21 \)

We can simplify the first equation by dividing by 4: \( m + 2v=\frac{53}{4} = 13.25 \), so \( m = 13.25 - 2v \)

Step3: Substitute into second equation

Substitute \( m = 13.25 - 2v \) into \( 2m + 3v = 21 \):
\( 2(13.25 - 2v)+3v = 21 \)
\( 26.5 - 4v + 3v = 21 \)
\( 26.5 - v = 21 \)
\( -v = 21 - 26.5 \)
\( -v = -5.5 \)
\( v = 5.5 \)

Step4: Find \( m \)

Substitute \( v = 5.5 \) into \( m = 13.25 - 2v \):
\( m = 13.25 - 2(5.5) \)
\( m = 13.25 - 11 \)
\( m = 2.25 \)

Answer:

Rental cost for each movie: $\boldsymbol{2.25}$
Rental cost for each video game: $\boldsymbol{5.5}$