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Algebra

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Here's another problem I'm having a little trouble with:

A piece of string is 40 cm long. It is cut into three pieces. The longest piece is 3 times as long as the middle-sized piece, and the shortest piece is 23 cm shorter than the longest piece. Find the lengths of the three pieces.

What could be an equation I could write?

Thank you so much!

  • Algebra -

    call the middle size m
    then the long piece is 3 m
    and the short piece is 3m-23
    so
    (3m-23) + m + 3m = 40
    7 m -23 = 40
    solve for m

  • Algebra -

    Thank you very much!

  • Algebra -

    7m - 23 =40
    + 23 +23
    then 7m=63
    then you divide 63 by 7 it equal 9
    so the ans. is m=9 :)

  • Algebra -

    How about:
    let the shortest piece be x cm

    <the shortest piece is 23 cm shorter than the longest piece> or
    the longest piece is 23 more than the shortest piece,
    so longest = x+23

    <The longest piece is 3 times as long as the middle-sized piece> or
    the middle piece is 1/3 of the longest piece,
    so middle piece = 1/3(x+23)

    then x + (x+23) + 1/3(x+23) = 40

    (I get x=4, for the shortest piece of 4 cm)

  • Algebra -

    Thanks!

  • Algebra -

    whats the answer?

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