An Age Enigma

Story:

1) Ten years from now Tim will be twice as old as Jane was when Mary was 
   nine times as old as Tim.

2) Eight years ago, Mary was half as old as Jane will be when Jane is one year
   older than Tim will be at the time when Mary will be five times as old as 
   Tim will be two years from now.

3) When Tim was one year old, Mary was three years older than Tim will be when 
   Jane is three times as old as Mary was six years before the time when Jane 
   was half as old as Tim will be when Mary will be ten years older than Mary 
   was when Jane was one-third as old as Tim will be when Mary will be three 
   times as old as she was when Jane was born.

Question: HOW OLD ARE THEY NOW?

Solution: Tim is 3, Jane is 8, and Mary is 15.

  A little grumbling
is in order here, as clue number 1 leads to the situation a year and a
half ago, when Tim was 1 1/2, Jane was 6 1/2, and Mary was 13 1/2.

This sort of problem is easy if you write down a set of equations.  Let
t be the year that Tim was born, j be the year that Jane was born, m be
the year that Mary was born, and y be the current year.  As indefinite
years come up, let y1, y2, ... be the indefinite years.  Then the
equations are


y + 10 - t = 2 (y1 - j)
y1 - m = 9 (y1 - t)

y - 8 - m = 1/2 (y2 - j)
y2 - j = 1 + y3 - t
y3 - m = 5 (y + 2 - t)

t + 1 - m = 3 + y4 - t
y4 - j = 3 (y5 - 6 - m)
y5 - j = 1/2 (y6 - t)
y6 - m = 10 + y7 - m
y7 - j = 1/3 (y8 - t)
y8 - m = 3 (j - m)

t = y - 3
j = y - 8
m = y - 15