One month Rita rented 7 movies and 9 video games for a total of $78. The next month she rented 5 movies and 3 video games for a total of $36. Find the rental cost for each movie and each video game.
+37159 7m + 9v = 78
5m + 3v = 36 multiply this equation by - 3
-15m - 9v = -108 add this equation to first
-8m = -30
m = 3.75 then v = 5.75
+230 From the following information in the problem, we construct the following equations: (assuming that we use m=movies and v=video games.)
1.7m+9v=78
2. 5m+3v=36
Using the method of substitution:
7m+5m+9v+3v=114
12m+12v=114
m+v=19/2
and so m=19/2-v.
Substituting this into equation 1, we get:
7(19/2-v)+9v=78
66.5+2v=78
2v=11.5
v=5.75 and so m=3.75
