Solving a word problem using linear equation

Question

One month Omar rented 3 movies and 5 video games for a total of $41. The next month he rented 12 movies and 2 video games for a total of $65. 

Find the rental cost for each movie and each video game.

Rental cost for each movie:

Rental cost for each game:

Answer 1

Let m be the cost of renting a movie and v be the cost of renting a video.

One month Omar rented 3 movies and 5 video games for a total of $41.

3m + 5v = 41

The next month he rented 12 movies and 2 video games for a total of $65. 

12m + 2v = 65

So your two equations are:

3m + 5v = 41

12m + 2v = 65

Can you solve it now? Use either substitution or elimination.

Answer 2

3M + 5V = 41

12M + 2V = 65

multiply 1st equation by 4 and subtract the 2nd equation to get

12M +20V = 164

12M + 2V =65

18V = 99

V = 99/18 = 11/2 = $5.50 per video game

3M + 5V = 41

3M = 41-5V = 41-27.5= 13.5

M = 13.5/3 = 4.5 = $4.50 per movie

Omar needs to watch more movies and do less video games to save money, unless

the movies are much shorter than a video game, then he might save more money

by playing more video games and watch less movies.