One month diane rented 2 movies and 12 video games for a total of $81. the next month she rented 5 movies and 3 video games for a total of $27. find the rental cost for each movie and each video game.

The rental cost for each movie = 1.5 $

The rental cost for each video game = 6.5 $

Explanation:

Let the rental cost for movie be a and video game be b.

One month Diane rented 2 movies and 12 video games for a total of $81

                      2 a + 12 b = 81 $ Equation 1

The next month she rented 5 movies and 3 video games for a total of $27

                      5 a + 3 b = 27 $ Equation 2

Equation 2 x 4,

                    20 a + 12 b = 108 $ Equation 3

 Equation 3 - Equation 1,

                    20 a + 12 b -  (  2 a + 12 b ) = 108 - 81

                     18 a = 27

                          a = 1.5 $

Substituting in equation 1

                   2 x 1.5 + 12 b = 81

                     12 b = 81 - 3

                         b = 6.5 $

The rental cost for each movie = 1.5 $

The rental cost for each video game = 6.5 $