Question

"One month Sam rented 12 movies and 2 video games for a total of $41. The next month he rented 3 movies and 5 video games for a total of $35 . Find the rental cost for each movie and each video game."

Answer 1

Movie price: $2.5

Video game price: $5.5

Explanation:

First month

12 movies (
`m`);

2 video games (
`v`);

Cost: $41

Second month

3 movies (
`m`);

5 video games (
`v`);

Cost: $35

`$\left \{ {{12m+2v=41} \atop {3m+5v=35}} \right.$`

`$\left \{ {{12m+2v=41} \atop {3(-4)m+5(-4)v=(-4)35}} \right.$`

`$\left \{ {{12m+2v=41} \atop {-12m+-20v=-140}} \right.$`

`-18v=-99`

`v=5.5`

`12m+2(5.5)=41`

`12m+11=41`

`12m=30`

`m=2.5`

Answer 2

Movies cost $2.50 and video games cost $5.50

Explanation:

Let the rental cost of movies be x and the rental cost of video games y

12x + 2y = 41

3x + 5y = 35

Solve by substitution