Answer:
To find the rental cost for each movie and video game, let's assign variables to represent the unknowns. Let's say the cost per movie is 'm' and the cost per video game is 'g'.
According to the information given, in the first month, Dan rented 12 movies and 2 video games for a total of $41. We can write this as an equation:
12m + 2g = 41 -- Equation 1
In the next month, he rented 3 movies and 5 video games for a total of $35. Again, we can write this as an equation:
3m + 5g = 35 -- Equation 2
Now, we have a system of two equations with two variables. We can solve this system to find the values of 'm' and 'g'.
Multiplying Equation 1 by 5 and Equation 2 by 2, we get:
60m + 10g = 205 -- Equation 3
6m + 10g = 70 -- Equation 4
By subtracting Equation 4 from Equation 3, we eliminate 'g':
(60m + 10g) - (6m + 10g) = 205 - 70
54m = 135
m = 135/54
m = 2.5
Now that we know the value of 'm' is 2.5, we can substitute it back into either Equation 1 or Equation 2 to find 'g'.
Let's substitute it back into Equation 1:
12m + 2g = 41
12(2.5) + 2g = 41
30 + 2g = 41
2g = 41 - 30
2g = 11
g = 11/2
g = 5.5
So, the rental cost for each movie is $2.5 and the rental cost for each video game is $5.5.