Question

One month Ivanna rented 3 movies and 5 video games for a total of $37. The next month she rented 12 movies and 2 video games for a total of 31$ find the rental cost for each movie and each video game.

Answer 1

To find the rental cost for each movie and video game, we set up a system of linear equations from Ivanna's rental costs. By using the elimination method to solve the system, we determined that the cost of renting one movie is $1.50 and the cost of renting one video game is $6.50.

Step-by-step explanation:

The question involves solving a system of linear equations to find the cost of individual items based on the total cost of multiple items over two periods. Specifically, we want to find the rental cost for each movie and each video game based on Ivanna's rental history.

Step-by-step Solution

1. Let's define the variables:
   M = cost of renting one movie
   V = cost of renting one video game
2. From the first month's rental, we can create the first equation based on the given information:
   
   3M + 5V = $37 (1)
3. From the second month's rental, we have the second equation:
   
   12M + 2V = $31 (2)
4. We solve the system of equations either by substitution or elimination methods. For this example, let's use the elimination method.
5. Multiply equation (1) by 4 to make the coefficient of V the same in both equations:
   
   12M + 20V = $148 (3)
6. Subtract equation (2) from equation (3):
   
   18V = $117
7. Solve for V:
   V = $117 / 18
   V = $6.50
8. Plug the value of V into equation (1) to find M:
   
   3M + 5($6.50) = $37
   
   3M + $32.50 = $37
   
   3M = $4.50
   M = $4.50 / 3
   M = $1.50

Therefore, the rental cost for each movie is $1.50 and each video game is $6.50.