SOLUTION: Diopanthes (born 250 A.D.)passed a sixth of his life in childhood, a twelfth in adolescence, and a seventh more as a bachelor; five years later, he got married, a son was born to h

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Question 243136: Diopanthes (born 250 A.D.)passed a sixth of his life in childhood, a twelfth in adolescence, and a seventh more as a bachelor; five years later, he got married, a son was born to him and died four years before Diopanthes at one-half his father's final age. What is his age from birth till Death ?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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Diopanthes (born 250 A.D.)passed a sixth of his life in childhood, a twelfth in adolescence, and a seventh more as a bachelor; five years later, he got married, a son was born to him and died four years before Diopanthes at one-half his father's final age. What is his age from birth till Death ?
:
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