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 ?

(In reply to How do you do these? by Gamer)

You take each phrase and look at what it says separately.

1) Old is twice as old as young was (L1=2(Y2)) [L1 =Old at time 1; Y2= Young at time 2]

2) when Old was half as old as Young will be (L2 = (Y3)/2)) [Immediately after a "when" give the same time subscript as immediately before the when.]

3) when Young is three times as old as Old was (Y3 = 3(L4))

4) when Old was three times as old as young (L4 = 3(Y4))

So we have 5 equations:

L1 + Y1 = 48
L1=2(Y2)
L2 = (Y3)/2
Y3 = 3(L4)
L4 = 3(Y4)

To which we can add three more
L1 - L4 = Y1 - Y4
L2 - L4 = Y2 - Y4
L3 - L4 = Y3 - Y4

since Lx and Yx represent their respective ages at time x, and they both age at the same rate.

So now we have the problem of solving 8 equations for 8 variables, and it becomes simple algebra.

Posted by TomM on 2003-05-26 18:54:34