Question 372808
Diohantius lived X years. He spent 1/6 of his life in boyhood, and 1/12 of his life as a youth.
 After 1/7 more of his life passed, he became married. 5 years later, he had a son.
 The son lived 1/2 as long as Dipohantus, and died 4 years before Diophantus died.
 How old was Diophantus? 
:
Let x = his final age
:
a lengthy but simple equation
Final age = child + youth + bach + marriage + son's age + 4 
x = {{{1/6}}}x + {{{1/12}}}x + {{{1/7}}}x + 5 + {{{1/2}}}x + 4 
:
Common denominator of 12*7 = 84
x = {{{14/84}}}x + {{{7/84}}}x + {{{12/84}}}x + 5 + {{{42/84}}}x + 4
:
x = {{{75/84}}}x + 9
:
{{{84/84}}}x - {{{75/84}}}x = 9
:
{{{9/84}}}x = 9
:
x = 84 is his final age
:
Check:
14 + 7 + 12 + 5 + 42 + 4 = 84