One month Ryan rented 4 movies and 8 video games for a total of $57. The next month he rented 2 movies and 3 video games for a total of $23. Find the rental cost for each movie and each video game.
Let's assume the cost of renting a movie is M and the cost of renting a video game is V.
From the information given, we can set up a system of equations:
4M + 8V = 57 (equation 1)
2M + 3V = 23 (equation 2)
To solve this system, we can use the method of substitution or elimination. Let's use the substitution method:
From equation 2, solve for M in terms of V:
2M = 23 - 3V
M = (23 - 3V)/2
Plug this expression for M into equation 1:
4[(23 - 3V)/2] + 8V = 57
46 - 6V + 8V = 57
-6V + 8V = 57 - 46
2V = 11
V = 5.5
Now, substitute the value of V back into equation 2 to find M:
2M + 3(5.5) = 23
2M + 16.5 = 23
2M = 23 - 16.5
2M = 6.5
M = 3.25
Therefore, the cost of renting a movie is $3.25 and the cost of renting a video game is $5.50.