one month charlie rented 2 movies 3 video games for a total of $21. The next month he rented 4 movies and 8 video games for a total of $53. Find the rental cost of each movies and each video game.
Accepted Solution
A:
x= cost per movie y= cost per video game
EQUATION 1: 2x + 3y= $21
EQUATION 2: 4x + 8y= $53
STEP 1: multiply equation 1 by -2.
-2(2x + 3y)= -2($21) -4x - 6y= -42
STEP 2: solve linear equations by elimination. use equation 2 and equation answer from step 1. add the two equations together. the x terms will cancel out. solve for y.
4x + 8y= 53 -4x - 6y= -42
2y= 11 divide both sides by 2 y= 11/2 divide y= $5.5 per video game
STEP 3: substitute y answer from step 2 into either original equation to solve for x. 2x + 3y= $21 2x + 3(5.50)= 21 2x + 16.50= 21 subtract 16.50 from both sides 2x= 4.50 divide both sides by 2 x= $2.25 per movie