SOLUTION: Diophantus spent 1/6 of his life in childhood, 1/12 as a youth, and 1/7 more as a bachelor. 5 years after his marriage was born a son who died 4 years before his father at 1/2 the

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Question 244899: Diophantus spent 1/6 of his life in childhood, 1/12 as a youth, and 1/7 more as a bachelor. 5 years after his marriage was born a son who died 4 years before his father at 1/2 the age at which his father died. How old was Diophantus when he died?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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Diophantus spent 1/6 of his life in childhood, 1/12 as a youth, and 1/7 more as a bachelor. 5 years after his marriage was born a son who died 4 years before his father at 1/2 the age at which his father died. 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%2F6x + 1%2F12x + 1%2F7x + 5 + 1%2F2x + 4
:
Common denominator of 12*7 = 84
x = 14%2F84x + 7%2F84x + 12%2F84x + 5 + 42%2F84x + 4
:
x = 75%2F84x + 9
:
84%2F84x - 75%2F84x = 9
:
9%2F84x = 9
:
x = 84 is his final age
:
Check:
14 + 7 + 12 + 5 + 42 + 4 = 84