Question 194190
"Diophantus passed 1/6 of his life in childhood, 1/12 in youth and 1/7 more
 as a bachelor. Five years after his marriage, was born a son who died 4 years
 before his father, at 1/2 his father's final age." How old was Diophantus when he died?
:
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
:
Multiply both sides by 84
9x = 84(9)
:
x = 84 is his final age
:
Check:
14 + 7 + 12 + 5 + 42 + 4 = 84