document.write( "Question 674243: Bob spent 1/6 of his life as a child, 1/12 as an adolescent, and 1/7 as a bachelor, five years after he was married, he had a son who died 4 years before his father at half his father's final age. How long did bob live? \n" ); document.write( "

Algebra.Com's Answer #852508 by ikleyn(53427) $\"\"$ $\"About$

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\n" ); document.write( "Bob spent 1/6 of his life as a child, 1/12 as an adolescent, and 1/7 as a bachelor,
\n" ); document.write( "five years after he was married, he had a son who died 4 years before his father
\n" ); document.write( "at half his father's final age. How long did bob live?
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\n" ); document.write( "\n" ); document.write( "Wording in your post is not perfect, but don't despair. There is a classic
\n" ); document.write( "well known story problem about Diophantus, famous mathematician of ancient Greece.\r
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document.write( "    Diophantus's youth lasts 1/6 of his life. He grew a beard after 1/12 more of his life. \r\n" );
document.write( "    After 1/7 more of his life, Diophantus married. Five years later, he had a son. \r\n" );
document.write( "    The son lived exactly half as long as his father, and Diophantus died just four years \r\n" );
document.write( "    after his son's death. What was his age when he died?\r\n" );
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\n" ); document.write( "\n" ); document.write( "This story problem is precisely what you want to follow literally. So, I will solve it for you.
\n" ); document.write( "Again, it is classic of about 2200 years old.\r
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document.write( "Let x be the Diophantus' age when he died.\r\n" );
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document.write( "As we read the problem, we write this equation\r\n" );
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document.write( "    x =  +  +  + 5 +  + 4.\r\n" );
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document.write( "To solve, multiply all the terms by the Greatest Common Denominator, which is 12*7 = 84.\r\n" );
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document.write( "You will get\r\n" );
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document.write( "    84x = 14x + 7x + 12x + 5*84 + 42x + 4*84.\r\n" );
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document.write( "Group like terms in right side\r\n" );
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document.write( "    84x = (14 + 7 + 12 + 42)x + (5*84 + 4*84),\r\n" );
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document.write( "combine like terms\r\n" );
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document.write( "    84x = 75x + 756,\r\n" );
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document.write( "simplify and find x\r\n" );
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document.write( "    84x - 75x = 756,\r\n" );
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document.write( "       9x     = 756,\r\n" );
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document.write( "        x     = 756/9 = 84.\r\n" );
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document.write( "Thus, Diophantus died at the age of 84 years.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "About Diophantus, read this remarkable Wikipedia article\r
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\n" ); document.write( "\n" ); document.write( "https://en.wikipedia.org/wiki/Diophantus\r
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\n" ); document.write( "\n" ); document.write( "https://en.wikipedia.org/wiki/Diophantus\r
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\n" ); document.write( "\n" ); document.write( "Enjoy ( ! )\r
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