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21 October, 11:22

The Jacobsen family bought concessions at the state fair. • Each hot dog costs $1.25. • Each hamburger costs $2.50. • The family bought a total of 13 hot dogs and hamburgers. • The family spent $22.50 on the hot dogs and hamburgers. Enter the number of hot dogs and hamburgers the Jacobsen family bought. Hot dogs hamburgers

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  1. 21 October, 14:09
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    The family bought 8 hot dogs and 5 hamburguers.

    Step-by-step explanation:

    We'll call the amount of hamburguers as 'x' and the amount of hot dogs as 'y'. Since the family bought 13 hot dogs and hamburguers we have:

    x + y = 13

    The family spent a total of 22.5, if each hot dog costs 1.25 and each hamburguer costs 2.5, we have:

    2.5*x + 1.25*y = 22.5

    We now have two equations and two variables so we can build a system as state bellow:

    x + y = 13

    2.5*x + 1.25*y = 22.5

    From the first equation we have x = 13 - y. We can use this value on the second equation to solve for y:

    2.5 * (13 - y) + 1.25*y = 22.5

    32.5 - 2.5*y + 1.25*y = 22.5

    -2.5*y + 1.25*y = 22.5 - 32.5

    -1.25*y = - 10

    y = 10/1.25 = 8

    So x = 13 - y = 13 - 8 = 5.

    The family bought 8 hot dogs and 5 hamburguers.
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