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Posers and Puzzles

Posers and Puzzles

  1. 25 Apr '05 12:23
    If the product of a woman's present age (W) and wedding age (w) is subtracted from the product of her husband's present age (M) and wedding age (m) and the result of this is added to (Wm-Mw) the result is 553. Find the present ages.
  2. Standard member PBE6
    Bananarama
    25 Apr '05 15:12
    I'm assuming that you're looking for an integer solution. If so, the man is presently 43 and the woman is 36. They have been married for 16 years.
  3. 25 Apr '05 15:45 / 2 edits
    Originally posted by elopawn
    If the product of a woman's present age (W) and wedding age (w) is subtracted from the product of her husband's present age (M) and wedding age (m) and the result of this is added to (Wm-Mw) the result is 553. Find the present ages.
    Mm - Ww + Wm - Mw
    = M(m - w) + W(m - w)
    = (M + W)(m - w)

    But M - m = W - w
    So m - w = M - W

    Hence (M + W)(M - W) = 553 = 79*7

    M = 43
    W = 36
  4. 25 Apr '05 15:51
    Originally posted by PBE6
    They have been married for 16 years.
    How do you get that? Seems to me that all you can get about their ages when married is the that he's 7 years older.
  5. Standard member royalchicken
    CHAOS GHOST!!!
    25 Apr '05 15:59
    Originally posted by Schumi
    How do you get that? Seems to me that all you can get about their ages when married is the that he's 7 years older.
    The current ages must sum to 79, and differ by 7.
  6. 26 Apr '05 08:05
    Originally posted by THUDandBLUNDER
    Mm - Ww + Wm - Mw
    = M(m - w) + W(m - w)
    = (M + W)(m - w)

    But M - m = W - w
    So m - w = M - W

    Hence (M + W)(M - W) = 553 = 79*7

    M = 43
    W = 36
    Yep that's it. Good work.

    If you still dont get it.....

    We have Mm-Ww+Wm-Mw = 553
    Hence M(m-w)+W(m-w) = 553
    Therefore (M + W)(m - w) = 553 = 7*79

    Let x be the number of years between the wedding and the present day. Then m = M-x, w = W-x and m-w = M-x-W+x = M-W

    Hence (M + W)(M - W) = 7*79

    Then either M+W = 553 ( this is not reasonable as the couple would be too old)

    or M+W = 79

    Then M-W = 7. Adding these gives 2M = 79+7 = 86 and M=43
    Then W = 43 - 7 = 36

    Basically what TB said. You should be able to get it now Schumi.