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 ?

You might find this solution a bit easier to follow (but maybe not!)

Define Old as x and Young as y

Now start at the end and work the other way: "when Old was 3x as old as Young". Let 'a' be how long ago that was and you get:

(x-a) = 3(y-a)

Now look at "when Young is 3x as old as Old was". Define 'b' to be how far into the future that is, and using the fact we just defined Old to be x-a we get:

(y+b) = 3(x-a)

Next "when Old was half as old as Young will be". Define 'c' to be how long ago that was, and we just said Young will be y+b we get:

(x-c) = 1/2(y+b)

Finally "Old is twice as old as Young was". We defined it to be c years ago, so Young was y-c and we get:

x = 2(y-c)

Now use x+y = 48 and you have your 5 equations in 5 unknowns. Use whatever algebra tool you like to solve. Matrices are fun.

Reading that over, that might not be that clear!

Posted by Jack Squat on 2004-01-20 12:12:27