math help please word problem

Question

One month Juan rented 

12

 movies and 

2

 video games for a total of 

$29

. The next month he rented 

3

 movies and 

5

 video games for a total of 

$32

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

Answer 1

First define the variables. m=cost of movie rental, v=cost of video rental. Then write the 2 equations

12m+2v=29

3m+5v =32. Then solve by elimination. Multiply the second equation by -4

-4(3m+5v=32) and you get

-12m -20v=-128 Then you add that to the first equation

12m+2v=29 and you get

-18v=-99 then you divide by 18 and get

v=$5.50

next you substitute to get m

12m+2(5.50)=29

12m+11=29 then you subtract 11 from both sides

12m+11-11=29-11

12m=18 Then you divide both sides by 12

M=1.50 So a video game costs $5.50 and a movie costs $1.50