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Math Help - Pumpkin Problem

  1. #1
    Newbie
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    Oct 2012
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    Union City
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    Pumpkin Problem

    Hello, I need help with the following problem:

    The cost of 2 large pumpkins plus 1 medium-sized pumpkin is the same as the cost of 8 small pumpkins. One large pumpkin costs the same as 1 medium sized pumpkin plus 1 small pumpkin. How many small pumpkins can you buy for the prize of a large pumpkin?

    I solved the problem but I want to make sure that I did it correctly:

    Prices

    x = large pumpkin
    y = medium pumpkin
    z = small pumpkin

    "cost of 2 large pumpkins plus 1 medium-sized pumpkin is the same as the cost of 8 small pumpkins"

    2x + y = 8z

    "One large pumpkin costs the same as 1 medium sized pumpkin plus 1 small pumpkin"

    x = y + z

    Using the substitution method to solve this system of equations:

    2x + y = 8z
    2(y + z) + y = 8z
    2y + 2z + y = 8z
    3y = 6z
    y = 2z

    Using the previous answer,

    x = y + z
    x = (2y) + z
    x = 3z

    Answer: You can buy 3 small pumpkins for the price of one large pumpkin.

    Is this correct guys?? Thanks for your help
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  2. #2
    MHF Contributor MarkFL's Avatar
    Joined
    Dec 2011
    From
    St. Augustine, FL.
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    Re: Pumpkin Problem

    Looks good to me.
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  3. #3
    Newbie
    Joined
    Oct 2012
    From
    Union City
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    Re: Pumpkin Problem

    Thanks!
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