Question

One month Ivanna rented 8 movies and 4 video games for a total of $57. The next month she rented 3 movies and 2 video games for a total of $24.
Find the rental cost for each movie and each video game.

Answer 1

Answer:

Step-by-step explanation:

X = Movies | Y = Video Games

Using these variables, we can set up equations.

3x + 2y = $24  eq1

 

8x + 4y = $57 eq2

We have here a system of equations, where we have two or more equations with two or more different variables.  We use the elimination method to solve for the variables.

 

Multiply eq1 by 8.  Multiply eq2 by 3.

24x + 16y = $192 eq1

24x + 12y = $171 eq2

Subtract eq2 from eq1 to eliminate the x terms.

4y = 21

y = $5.25

This rental cost of one video game is $5.25

Substitute the value of y into eq1 to solve for x.  This will give you the rental cost of one movie.

The rental cost of one movie is $4.50

3($4.50) + 2($5.25) = $24

 

8($4.50) + 4($5.25) = $57