Find the rental cost for each movie and each video game

Question

One month Miguel rented 3 movies and 5 video games for a total of $42. The next month he rented 9 movies and 7 video games for a total of $72. Find the rental cost for each movie and each video game.

Answer 1

You are trying to find the values of two quantities, so you will need to set up a system of two equations in two variables. We'll call M the price of a move and V the price of a video game.

 

The first month: 3 movies, 5 video games, $42. Let's translate this into algebra:

 

3M + 5V = 42

 

The second month: 9 movies, 7 video games, $72. Translated:

 

9M + 7V = 72

 

Solve that system of equations.

Answer 2

Let x = the cost of a movie

Let y = the cost of a game

 

Using these variables, we can set up equations.

 

3x + 5y = 42                 eq1

 

9x + 7y = 72                 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 3.  Keep eq2.

 

9x + 15y = 126              eq1

9x + 7y = 72                 eq2

 

 

Subtract eq2 from eq1 to eliminate the x terms.

 

8y = 54

 

  y = 6.75

 

 

This rental cost of one video game is $6.75

 

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