Question 469231
 He was a boy for 1/6 of his life. after 1/12 more, he acquired a beard. After another 1/7, he married. in the fifth year of marriage, his son was born. The son lived half as many years as his father. Diaphanous died 4 years after his son. How old was Diaphanous 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
:
x = 84 is his final age
:
Check:
14 + 7 + 12 + 5 + 42 + 4 = 84