SOLUTION: the tomb of Diophantus here lies a great man. Mathematically his life is heroen inscribed for all to witness: One-quarter of his life was spent as a boy and a young man. then whe

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Question 101190: the tomb of Diophantus
here lies a great man. Mathematically his life is heroen inscribed for all to witness:
One-quarter of his life was spent as a boy and a young man. then when 1/7 of his life had passed he entered into matrimony, and 5 years later a son was born to him . Alas! when his son had reached only 1/2 his father's allotted time on this earth, death took him into its arms. to console himself while grieving over his son's death, he explired then discovered this science of numbers during a period of 4 years, after which, Diophantus passed on to a better world.
What was his life span?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=his age when he died (ie his life span)

%281%2F4%29x%2B%281%2F7%29x%2B5%2B%281%2F2%29x=x Translate the following word problem


7x%2B4x%2B140%2B14x=28x Multiply both sides by the LCD 28 to make every number a whole number




7x%2B4x%2B140%2B14x=28x Start with the given equation


25x%2B140=28x Combine like terms on the left side


25x=28x-140Subtract 140 from both sides


25x-28x=-140 Subtract 28x from both sides


-3x=-140 Combine like terms on the left side


x=%28-140%29%2F%28-3%29 Divide both sides by -3 to isolate x



x=140+%2F+3 Reduce

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Answer:
So our answer is x=140+%2F+3 (which is x=46.6666666666667 in decimal form)



So the father was about 47 when he died