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2 September, 08:18

One month Donna rented 5 movies and 6 video games for a total of $48. The next month she rented 3 movies and 2 video games for a total of $18. Find the

rental cost for each movie and each video game.

Rental cost for each movie: s]

x

5

?

Rental cost for each video game: S

+2
Answers (1)
  1. 2 September, 11:32
    0
    Cost for each movie: $1.50 Cost for each video game: $6.75

    Step-by-step explanation:

    Let x be the cost (in dollars) of renting a movie.

    Let y be the cost (in dollars) of renting a video game.

    The total cost of renting 3 movies and 2 video games is + 3x2y dollars.

    We're given that this total cost is $18, so we have = + 3x2y18.

    The total cost of renting 5 movies and 6 video games is + 5x6y dollars.

    We're given that this total cost is $48, so we have = + 5x6y48.

    Therefore, we get the following system of equations.

    =+3x2y18

    =+5x6y48

    Multiplying the first equation by - 3 and adding gives us the following.

    -9 x - 6 y = - 54 5 x + 6 y = 48 - 4 x + 0 y = - 6

    So we get the equation = -4x-6.

    Solving for x, we get the following.

    =x1.5

    To find y, we can substitute 1.5 for x in = + 3x2y18, the first equation in the system.

    Then we solve for y.

    +31.52y = 18

    +4.52y = 18

    2y = 13.5

    y = 6.75

    So, we have found that = x1.5 and = y6.75.

    This means that the rental cost for each movie is $1.50 and the rental cost for each video game is $6.75.
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