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21 June, 15:54

Juan and Adam go to the movie theater and purchase refreshments for their friends,

Juan spends a total of $130.00 on 10 bags of popcorn and 10 drinks.

Adam spends a total of $56.50 on 3 bags of popcorn and 5 drinks.

Write a system of equations that can be used to find the price of one bag of popcorn

and the price of one drink.

Using these equations, determine and state the price of a drink, to the nearest cent.

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Answers (2)
  1. 21 June, 17:35
    0
    Popcorn = $4.25 per bag, Drink = $8.75

    Step-by-step explanation:

    p = popcorn

    d = drinks

    10p + 10d = 130

    3p + 5d = 56.50

    multiply the second equation by - 2 and then solve by elimination

    -6p - 10d = - 113

    4p = 17

    p = 4.25

    3 (4.25) + 5d = 56.50

    5d = 43.75

    d = 8.75
  2. 21 June, 18:21
    0
    10x + 10y = $130.00

    3x + 5y = $56.50

    Solution: x=4.25 and y=8.75

    Step-by-step explanation:

    The variable x will be used here to show the price of each bag of popcorn, while y will be used to represent the price of each drink. First we can solve 10x + 10y = 130 for x:

    10x + 10y = 130

    10x + 10y + - 10y = 130 - 10y (Subtract 10y from both sides)

    10x = - 10y + 130

    Now divide 10 by both sides

    x = - y + 13

    Next, you will substitute - y + 13 for x in 3x + 5y = 56.5:

    3x + 5y = 56.5

    3 (-y + 13) + 5y = 56.5

    2y + 39 = 56.5 (Simplify both sides of the equation)

    2y + 39 + - 39 = 56.5 + - 39 (Add - 39 to both sides)

    2y = 17.5 (Now divide both sides by 2)

    y = 8.75

    You can check this by substituing 8.75 for y in x = - y + 13
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