SOLUTION: Diophantus a greek mathematician is considered by many as the "Father of Algeria" because of his works in the syncopation of algebra. In his epitaph, the following is scripted. "A

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Question 221258: Diophantus a greek mathematician is considered by many as the "Father of Algeria" because of his works in the syncopation of algebra. In his epitaph, the following is scripted. "A sixth of his life was spent in childhood. A twelfth as a youth, and a seventh as a bachelor. Five years after his marriage, his son was born but died four years before his own death at half his age".
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Diophantus passed one-sixth of his life in childhood, one-twelfth in youth, one-seventh more as a bachelor. Five years after his marriage, a son was born who died four years before his father, at half 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
:
x = 84 is his final age
:
Check:
14 + 7 + 12 + 5 + 42 + 4 = 84