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Brain teaser?

  1. Mar 6, 2004 #1
    Can anyone solve this puzzle that a friend sent to me?

    When Ann is half as old as Mary will be when Mary is three times as old as Mary is now. Mary will be five times as old as Ann is now. Neither Ann nor Mary may vote. How old is Ann?
     
  2. jcsd
  3. Mar 6, 2004 #2

    matt grime

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    let the ages be A and M in hte obvious fashion, and suppose that this point in the future when the ages have this property is k years away, then translating


    A+k= 3M/2

    (at this point when anne is k years older, he age is 3/2 of mary's current age)

    simultaneously,

    M+k=5A

    mary is 5 times as old as anne is.

    comparing and eliminating the k,

    5M=12A

    we're presuming that M and A rea integers less than 18. So as 12 is prime to 5, it muust be that M is a multiple of 12, and the only one that assures minority is M=12, and hence A=5.
     
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