Algebra 1 question

Question

One month Dan rented 8 movies and 4 video games for a total of $49 . The next month he rented 3 movies and 2 video games for a total of $21 . Find the rental cost for each movie and each video game

Answer 1

Let M = movie cost

Let V = video game cost 

 

8*M + 4*V = 49

3*M + 2*V = 21

 

Multiply the 2nd equation by (-2) and then add the 2 equations together 

 

8*M + 4*V = 49

-6*M - 4*V = -42

 

2*M + 0*V = 7

M = 7/2 = 3.50

 

Plug this value for M into the original 2nd equation and solve for V 

 

3*(7/2) + 2*V = 21

21/2 + 2*V = 21

21 + 4*V = 42

4*V = 21

V = 21/4 = 5.25 

 

So a movie costs $3.50 and a video games costs $5.25 

 

Check:  8*(3.50) + 4*(5.25) = 28 + 21 = $49

            3*(3.50) + 2*(5.25) = 10.50 + 10.50 = $21