At a concession stand five hot dogs and four hamburgers cost $12 for hot dogs and five hamburgers cost 1275 the cause of one hot dog in the

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At a concession stand five hot dogs and four hamburgers cost $12 for hot dogs and five hamburgers cost 1275 the cause of one hot dog in the cost of one hamburger

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Lydia 20 hours 2021-10-12T22:01:39+00:00 1 Answer 0

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    2021-10-12T22:02:59+00:00

    Answer:

    The cost of one hot dog $1 and the cost of one hamburger is $1.75.

    Step-by-step explanation:

    Given:

    At a concession stand five hot dogs and four hamburgers cost $12.

    Four hot dogs and five hamburgers cost $12.75.

    Now, to find the cost of one hot dog and the cost of one hamburger.

    Let the cost of one hot dog be x.

    And let the cost of one hamburger be y.

    So, the cost of five hot dogs and four hamburgers:

    5x+4y=12\\\\  

    4y=12-5x  

    Dividing both sides by 4 we get:

    y=3-\frac{5x}{4}   …….(1)

    And, the cost of four hot dogs and five hamburgers:

    4x+5y=12.75  

    Substituting the value of y from equation (1):

    4x+5(3-\frac{5x}{4})=12.75

    4x+15-\frac{25x}{4}=12.75

    4x-\frac{25x}{4}+15 =12.75

    \frac{16x-25x}{4}+15=12.75

    \frac{-9x}{4} +15=12.75

    Subtracting both sides by 15 we get:

    \frac{-9x}{4}=-2.25

    Multiplying both sides by 4 we get:

    -9x=-9

    Dividing both sides by -9 we get:

    x=1.

    The cost of one hot dog  = $1.

    Now, substituting the value of x in equation (1):

    y=3-\frac{5x}{4}

    y=3-\frac{5\times 1}{4}

    y=3-\frac{5}{4}

    y=3-1.25

    y=1.75.

    The cost of one hamburger = $1.75.

    Therefore, the cost of one hot dog $1 and the cost of one hamburger is $1.75.

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