Algebra

At a concession stand three hot and 4 hamburgers cost 13.50; 4 hot dogs and 3 numbers cost 12.75. Find the cost one hot dog and the cost of one hamburger

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  1. x = the cost of hot dog

    y = the cost of hamburger

    3 x + 4 y = 13.5

    4 x + 3 y = 12.75

    3 x + 4 y = 13.5

    -

    4 x + 3 y = 12.75
    ______________________

    - x + y = 0.75 Add x to both sides

    - x + y + x = 0.75 + x

    y = 0.75 + x

    4 x + 3 y = 12.75

    4 x + 3 * ( 0.75 + x ) = 12.75

    4 x + 2.25 + 3 x = 12.75

    7 x + 2.25 = 12.75 Subtract 2.25 to both sides

    7 x + 2.25 - 2.25 = 12.75 - 2.25

    7 x = 10.5 Divide both sides by 7

    x = 10.5 / 7 = 1.5

    y = 0.75 + x = 1.5 + 0.75 = 2.25

    the cost of hot dog = 1.5
    the cost of hot hamburger = 2.25

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