The rental cost of each movie is $4.50
The rental cost of each video game is $5.75
Step-by-step explanation:
let the cost of one movie = m
let the cost of one video games = v
1st month:
Number of movies = 5
number of video games = 6
Total cost of both = $57
Total cost = cost of one movie(Number of movies ) + cost of one video (Number of video games)
57 = m(5) + v(6)
57 = 5m + 6v ...equation 1
2nd month:
Number of movies = 3
number of video games = 2
Total cost of both = $25
Total cost = cost of one movie(Number of movies ) + cost of one video (Number of video games)
25 = m(3) + v(2)
25 = 3m + 2v ...equation 2
57 = 5m + 6v ...equation 1
25 = 3m + 2v ...equation 2
Using elimination method:
To eliminate v, we would multiply equation 2 by 3:
3(25) = 3(3m) + 3(2v) ...equation 2
75 = 9m + 6v ...equation 2
57 = 5m + 6v ...equation 1
subtract equation 1 from 2:
75 - 57 = 9m - 5m + 6v - 6v
18 = 4m + 0
18 = 4m
m = 18/4
m = 4.5
Substitute for m in any of the equation:
Using eqauation1: 57 = 5m + 6v
57 = 5(4.5) + 6v
57 = 22.5 + 6v
57 - 22.5 = 6v
34.5 = 6v
v = 34.5/6
v = 5.75
The rental cost of each movie is $4.50
The rental cost of each video game is $5.75