MATH SOLVE

2 months ago

Q:
# 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

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! :)

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! :)