The combined ages of Mary and Ann are 44 years, and Mary is twice as old a Ann was when Mary was half as old as Ann will be when Ann is three times as old as Mary was when Mary was three times ad old as Ann. How old is Mary?

The age of Mary to that of Ann must be as 5 to 3. And as the sum of their ages
was 44, Mary was 27½ and Ann 16½. One is exactly 11 years older than the other.
I will now insert in brackets in the original statement the various ages specified:
"Mary is (27½) twice as old as Ann was (13¾) when Mary was half as old (24¾)
as Ann will be (49½) when Ann is three times as old (49½) as Mary was (16½)
when Mary was (16½) three times as old as Ann (5½)." Now, check this backwards.
When Mary was three times as old as Ann, Mary was 16½ and Ann 5½ (11 years younger).
Then we get 49½ for the age Ann will be when she is three times as old as Mary was then.
When Mary was half this she was 24¾. And at that time Ann must have been 13¾ (11 years younger).
Therefore Mary is now twice as old -- 27½, and Ann 11 years younger -- 16½.

Sorry I didn't look at this sooner, I've been out of civilization for a few weeks vacationing. Anyway.... Congrats to all three of you! You all got it right! Mary is 27 1/2 ears old. I kinda feel bad now since I was only able to figure out the answer by cheating and looking at the answers in my "MENSA Brain Bafflers" book...

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The age of Mary to that of Ann must be as 5 to 3. And as the sum of their ages was 44, Mary was 27½ and Ann 16½. One is exactly 11 years older than the other. I will now insert in brackets in the original statement the various ages specified: "Mary is (27½) twice as old as Ann was (13¾) when Mary was half as old (24¾) as Ann will be (49½) when Ann is three times as old (49½) as Mary was (16½) when Mary was (16½) three times as old as Ann (5½)." Now, check this backwards. When Mary was three times as old as Ann, Mary was 16½ and Ann 5½ (11 years younger). Then we get 49½ for the age Ann will be when she is three times as old as Mary was then. When Mary was half this she was 24¾. And at that time Ann must have been 13¾ (11 years younger). Therefore Mary is now twice as old -- 27½, and Ann 11 years younger -- 16½.

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Mary is 27.5 years old.

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Sorry I didn't look at this sooner, I've been out of civilization for a few weeks vacationing. Anyway.... Congrats to all three of you! You all got it right! Mary is 27 1/2 ears old. I kinda feel bad now since I was only able to figure out the answer by cheating and looking at the answers in my "MENSA Brain Bafflers" book...

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