One month dan rented 5 movies and 3 video games for a total of $37. The next month he rented 2 movies and 6 video games for a total of $40. Find the rental cost for each movie and each video game.

Answer 1

We have 2 variables (cost of movie and cost of video game) and we need 2 equations to find them. Let's say the cost of movies is M and the cost of video games is V. In the first month, Dan rented 5 movies (5M) and 3 video games (3V) for $37.

5M + 3V = 37 (equation 1)

The next month, he rented 2 movies and 6 games for $40.

2M + 6V = 40 (equation 2)

Let's isolate one of the variables. I choose to isolate M in equation 2:

M = (40 - 6V) / 2 = 20 - 3V

Now, substitute our new equation 2 into equation 1.

5*(20 - 3V) + 3V = 37

100 - 15V + 3V = 37

100 - 37 = 15V - 3V

63 = 12V

V = $5.25

Now, substitute the value of V into one of our earlier equations to find M.

M = 20 - 3V = 20 - 3*5.25

M = $4.25