The ages of Old and Young total 48. Old is twice as old as Young was when Old was half as old as Young will be when Young is three times as old as Old was when Old was three times as old as Young.

How old is Old ?

Let Old's age be L so as not to confuse with zero, and Young's age by Y.

First, how long ago (t years) was Old 3x as old as Young?
3(Y-t)=L-t
which gives t = (3Y-L)/2 years ago,
at which time Old was L - (3Y-L)/2

Young will be three times that when she is
3(L-(3Y-L)/2)
When Old was half that age he was
3(L-(3Y-L)/2)/2

At that time, since the difference in their ages remains constant, Young was
3(L-(3Y-L)/2)/2 - (L - Y)

Since Old is now twice this he is
3(L-(3Y-L)/2) - 2L + 2Y
which equals
5L/2 - 5Y/2

That's L = 5L/2 - 5Y/2, or 2L=5L-5Y but we also know that L+Y=48. Solving these simultaneously gives us Y = 18 and L = 30, that is, Young is 18 and Old is 30.

Posted by Charlie on 2003-05-24 04:59:16