If 2 sodas and 3 hot dogs are $17 while 5 sodas and 6 hot dogs are $38.75 – how much are each separately?

Question

If 2 sodas and 3 hot dogs are $17 while 5 sodas and 6 hot dogs are $38.75 – how much are each separately?

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Peyton 2 weeks 2021-09-28T08:27:21+00:00 1 Answer 0

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    2021-09-28T08:29:06+00:00

    Answer:

    Soda = $4.75

    Hotdog = $2.5

    Step-by-step explanation:

    Let the price for soda be A and that of hotdog be B

    2 sodas and three hotdogs are $17.

    That’s

    2A + 3B = 17

    Also, 5 sodas and 6 hotdogs are $38.75

    That’s

    5A + 6B = 38.75

    We now have two equations

    Equation 1: 2A + 3B = 17

    Equation 2: 5A + 6B = 38.75

    Multiply equation 1 by 5 and equation 2 by 2

    We have

    5 x 2A + 5 x 3B = 5 x 17

    2 x 5A + 2 x 6B = 2 x 38.75

    10A + 15B = 85

    10A + 12B = 77.5

    Subtract equation two from equation one

    3B = 7.5

    Divide both sides by 3

    B = 7.5/3

    B = 2.5

    Now substitute 2.5 for B in either of the equations to get A.

    Using equation 1 , we have

    2A + 3B = 17

    2A + 3 x 2.5 = 17

    2A + 7.5 = 17

    Subtract 7.5 from both sides

    2A + 7.5 – 7.5 = 17 – 7.5

    2A = 9.5

    Divide both sides by by 2

    A = 9.5/2

    A = 4.75

    Each soda cost $4.75 while each hotdog cost $2.5

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