Solving a word problem using a system of linear equations of the form Ax + By = C

Question

One month Karen rented 5 movies and 3 video games for a total of $37. The next month she rented 2 movies and 6 video games for a total of $40. Find the rental cost for each movie and each video game.

Answer 1

(1) 5m+3v=37, 

2m+6v=40, so m+3v=20, where m=rental cost of movie and v=rental cost of video.

(1)-(2): 4m=17, m=17/4=$4.25.

Therefore 4.25+3v=20, 3v=20-4.25=$15.75, v=15.75/3=$5.25.

Movie costs $4.25 and video costs $5.25.