Question

one month Ashley rented 3 movies and 5 video games for $38. The next month she rented 12 movies and 2 video games for a total of $53. Find the rental cost for each movie and each video game.

Answer 1

Let m and v represent the cost of a movie rental and a video rental.

Then 3m + 5v = $38 and 12m + 2v = $53. Solve this system of linear equations:

3m + 5v = $38

12m + 2v = $53

Let's eliminate m. Mult. the first eqn by -4, obtaining -12m - 20v = $152.

Now add this result to the 2nd equation:

-12m - 20v = -$152

12m + 2v = $53

---------------------------

-18v = -$99

Solving this for v, the cost of renting one video, is v = $99/18, or $5.50.

Now sub $5.50 for v in 3m + 5v = $38:

3m + $27.50 = $38. Then m, the cost of renting one movie, is $10.50.