a boy purchased a party-length sandwich 57 inches long. he wants to cut it into three pieces so that the middle piece is 6inches longer than the shortest piece and the shortest piece is 9 inches shorter than the longest price. how long should the three pieces be?

Let the longest piece be l. The middle piece be m. And the short piece be s. We have 2 equations in terms of the shortest piece:

  • l = s + 9 (Since the shortest piece is 9 inches shorter, this means the longest piece is 9 inches longer)
  • m = s + 6
  • s + m + l = 57
    • We substitute equations (1) and (2) into equation (3):
    s + (s + 6) + (s + 9) = 57

    Group like terms:
    (1 + 1 + 1)s + (6 + 9) = 57
    3s + 15 = 57

    To solve for s, we type this equation into our search engine and we get:
    s = 14

    Plug s = 14 into equation 2 to solve for m:
    m = 14 + 6
    m = 20

    Plug s = 14 into equation 1 to solve for l:
    l = 14 + 9
    l = 23

    Check our work for equation 3:
    14 + 20 + 23 ? 57
    57 = 57 <-- checks out

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