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One month Reuben rented 5 movies and 2 video games for a total of $23. The next month he rented 3 movies and 8 video games for a total of $58. Find the rental cost for each movie and each video game.

User Sasha Davydenko
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1 Answer

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12 votes

Answer:

Rental cost of each movie = $2

Rental cost of each video game = $6.5

Explanations:

Let the rental cost of each movie be "x"

Let the rental cost of each video game be "y"

If in one month Reuben rented 5 movies and 2 video games for a total of $23, this can be expressed as:

5x + 2y = 23 .............................. 1

If in the next month he rented 3 movies and 8 video games for a total of $58, then;

3x + 8y = 58 ............................... 2

Solve the equations simultaneously using the elimination method

5x + 2y = 23 .............................. 1 * 4

3x + 8y = 58 ............................... 2 * 1

Multiply equation 1 by 4 and equation 2 by 1 to have;

20x + 8y = 92 .............................. 3

3x + 8y = 58 ............................... 4

Subtract equation 3 from 4

20x - 3x = 92 - 58

17x = 34

x = 34/17

x = 2

Substitute x = 2 into equation 1 to get the value of "y"

Recall that 5x + 2y = 23

5(2) + 2y = 23

10 + 2y = 23

2y = 23 - 10

2y = 13

y = 13/2

y = 6.5

This shows that the rental cost of each movie is $2 and the rental cost of each video game is $6.5

User BlackHoleDetector
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