SOLUTION: Diophantus's youth lasted one sixth of his life. He grew a beard after one twelfth more. After one seventh more of his life, he married. 5 years later, he and his wife had a son

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Question 781909: Diophantus's youth lasted one sixth of his life. He grew a beard after one twelfth more. After one seventh more of his life, he married. 5 years later, he and his wife had a son. The son lived exactly one half as long as his father, and Diophantus died four years after his son.
How many years did Diophantus live?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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Diophantus's youth lasted one sixth of his life.
He grew a beard after one twelfth more.
After one seventh more of his life, he married.
5 years later, he and his wife had a son.
The son lived exactly one half as long as his father, and Diophantus died four years after his son.
How many years did Diophantus live?

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 = 9 * 84%2F9
:
x = 84 is his final age
:
Check:
14 + 7 + 12 + 5 + 42 + 4 = 84