Diophantus' Lifespan

Date: 05/14/97 at 22:09:17
From: Bonnie L Struble
Subject: Diophantus'  Life Span Problem

Diophantus' youth lasted 1/6 of his life. He grew a beard after 1/12
more of his life. After 1/7 more of his life, Diophantus married.  
Five years later he had a son. The son lived exactly 1/2 as long as 
his father, and Diophantus died just four years after his son's death.  
How many years did Diophantus live? 

I need to find an algebraic equation that will find the number of 
years Diophantus lived. Can you help me?  I have been stuck on this 
forever and the ways that I have been trying to solve it make 
absolutely no sense to me or my teacher. Please help!

Date: 05/15/97 at 11:02:44
From: Doctor Mitteldorf
Subject: Re: Diophantus'  Life Span Problem

Dear Bonnie,
  
Diophantus' son was born after 1/6 + 1/12 + 1/7 of his life plus 5 
years. The son died 4 years before Diophantus, and lived half as long.  

Let's write everything in terms of the number of years Diophantus 
lived, and call that x.  Then the son was born in year:

   (1/6 + 1/12 + 1/7 ) x + 5

The son died in year x-4.

Subtract the year of birth from the year of death, and you get the 
son's lifespan, which was half his father's:

   (x-4) - [ (1/6 + 1/12 + 1/7 ) x + 5 ]  =  x/2

Can you solve this equation?  

-Doctor Mitteldorf,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/