Question

One month Jessica rented 4 movies and 8 video games for a total of $61. The next month she rented 2 movies and 3 video games for a total of $25. Find the rental cost for each movie and each video game.

Answer 1

A movie costs $4.25 and a video game $5.5.

Explanation:

Step 1: Form the equations.

Let m be the price of a movie and v the price of the video game.

First equation: One month Jessica rented 4 movies and 8 video games for a total of $61.

`4m + 8v = 61`

Second equation: The next month she rented 2 movies and 3 video games for a total of $25.

`2m + 3v = 25`

Step 2: Solve the system of equations.

`\text{(1.) } 4m + 8v = 61\\\text{(2.) } 2m + 3v = 25`

I'm going to solve them by elimination. I'll multiply the second equation with two so I get 4m.

`\text{(1.) } 4m + 8v = 61\\\text{(2.) } 4m + 6v = 50`

Now I'm going to subtract the second equation from the first.

`(4m + 8v) - (4m + 6v) = 61 - 50`

And solve.

`8v- 6v = 61 - 50\\2v = 11\\v = (11)/(2)\\v = \$5.5`

Now let's insert v back in second equation to get m (nicer numbers, you can insert in first too if you want).

`4m + 8v = 61\\4m + 8(5.5) = 61\\4m + 44 = 61\\4m = 61 - 44\\4m = 17\\m = (17)/(4)\\m = \$4.25`