SOLUTION: "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

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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?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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"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%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
:
Multiply both sides by 84
9x = 84(9)
:
x = 84 is his final age
:
Check:
14 + 7 + 12 + 5 + 42 + 4 = 84