SOLUTION: 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

Algebra ->  Human-and-algebraic-language -> SOLUTION: 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      Log On


   

Question 156081This question is from textbook
: 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. This question is from textbook

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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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