The case of Mary and Ann

Who wants to have a little algebra fun? OK here we go:
The sum of the ages of Mary and Ann is 44. Mary is twice as old as Ann was when Mary was half as old as Ann will be when she is three times as old as Mary was when she was three times as old as Ann. How old are Mary and Ann?
My high school maths teacher took about 2 or 3 minutes to solve this when I presented it to him. It took me about 3 hours! (I never was a good student). If you get fed up, I'll post the answers here in a few days. I won't show the working out because it takes a while. And yes, it's possible to do without a calculator. If you'd like a clue read on:


It helps if you work through it backwards.

Originally posted by Mr Nice Guy
Who wants to have a little algebra fun? OK here we go:
The sum of the ages of Mary and Ann is 44. Mary is twice as old as Ann was when Mary was half as old as Ann will be when she is three times as old as Mary was when she was three times as old as Ann. How old are Mary and Ann?
My high school maths teacher took about 2 or 3 minutes to solve thi ...[text shortened]... out a calculator. If you'd like a clue read on:


It helps if you work through it backwards.

tricky...did it in 12 minutes. to preserve i will write the answer with a series of numbers pick every 4th number to see the answer

M=784246071821/2454

A=094189360981/2543

was i right? if you cant work my answer out of that mini puzzle lol i will PM it 2 u?

fred

Originally posted by Mr Nice Guy
Who wants to have a little algebra fun? OK here we go:
The sum of the ages of Mary and Ann is 44. Mary is twice as old as Ann was when Mary was half as old as Ann will be when she is three times as old as Mary was when she was three times as old as Ann. How old are Mary and Ann?

I'm not sure fractional ages make sense, but I calculate Ann's age to be 16.5 and Mary's age to be 27.5.

Mary (27.5) is twice as old as Ann was (2.75 years ago, or 13.75) when Mary (24.75) was half as old as Ann will be (33 years from now, or 49.5) when she is three times as old as Mary was (11 years ago, or 16.5) when she was three times as old as Ann (5.5).

Yeah, that's the answer. You guys nailed it.