Question

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.

Answer 1

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


CHECK:
4x + 8y= $53
4(2.25) + 8(5.50)= 53
9 + 44= 53
53= 53


ANSWER: The cost per movie is $2.25 and the cost per video game is $5.50.

Hope this helps! :)