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"Age" Word Problems (page 2 of 2) "Here lies Diophantus,"
the wonder behold . . .
Find Diophantus' age at death. My first task is to "translate" the poetry from the headstone into practical terms:
I will let d stand for Diophantus' age at death. Then: childhood: ^{d}/_{6}
His whole life had been
divided into intervals which, when added together, give the sum of his
life. So I'll add the lengths of those periods, set their sum equal
to his (asyet unknown) total age, and solve: .^{d}/_{6}
+ ^{d}/_{12} + ^{d}/_{7}
+ 5 + ^{d}/_{2} + 4 = d
Diophantus lived to be 84 years old. You can check the answer if you like, by plugging "84" into the original problem. If he lived to be 84, then onesixth of his life is 14 years, onetwelfth of his life is 7 years (so he'd be 21, and he certainly should have a beard by this age), oneseventh of his life is 12 years (so he didn't marry until he was 33 years old), his child was born when he was 38, the boy died at 42 (when Diophantus was 80), and then Diophantus died four years later. Always try to label your variables and expressions clearly, as this will go a long way toward helping you get your equations set up correctly. And remember that you can always check your answers (like I did on the last example above); checking your answers is an especially good idea on tests. << Previous Top  1  2  Return to Index



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