Challenging Age Problem with System of Equations

Date: 01/30/2005 at 18:19:27
From: Sean
Subject: insane two variable equation

A man is three times as old as his son was at the time when the 
father was twice as old as his son will be two years from now.  Find 
the present age of each if they sum to 55.

It just involves too many clauses - I can't make sense of it!

Date: 01/31/2005 at 12:09:51
From: Doctor George
Subject: Re: insane two variable equat

Hi Sean,

Thanks for writing to Doctor Math.

It may be easiest to think of this problem as having 3 variables. Here
are the variables.

   F = Father's age today
   S = Son's age today
   n = some number of years ago

Now we need three equations. We get them by translating each main idea
from English into algebra.

1. A man is three times as old as his son was n years ago.
   F = 3(S - n)

2. n years ago the father was twice as old as his son will be two
years from now.
   F - n = 2(S + 2)

3. The sum of their ages is 55.
   F + S = 55

Can you take it from here? Write again if you need more help.

- Doctor George, The Math Forum
  http://mathforum.org/dr.math/