document.write( "Question 158504: about all we know of Diophantus personal life is that contained in the following summary of ipitaph given in the greek Anthology. Diophantus passed onesix of his life in childhood, one twelve in youth and one seventh more as a bachelor. Five years after his marriage was born a son who died four years before his father, at half his father, at half his father's {final)age. How old was Diophantus when he died. \n" ); document.write( "

Algebra.Com's Answer #116769 by Edwin McCravy(20056) $\"\"$ $\"About$

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About all we know of Diophantus personal life is that contained in the following summary of ipitaph given in the greek Anthology. Diophantus passed one sixth of his life in childhood, one twelfth in youth and one seventh more as a bachelor. Five years after his marriage was born a son who died four years before his father, at half his father, at half his father's {final)age. How old was Diophantus when he died.\r
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document.write( "Suppose Diophantus was N years old when he died.\r\n" );
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document.write( ">>...Diophantus passed one sixth of his life in childhood,...<<\r\n" );
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document.write( "His childhood lasted  years.  Therefore,\r\n" );
document.write( "he was  years old when his childhood ended.\r\n" );
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document.write( ">>...one twelfth in youth...\r\n" );
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document.write( "His youth lasted  years so he was  years \r\n" );
document.write( "old when his youth ended.\r\n" );
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document.write( ">>...and one seventh more as a bachelor...<\r\n" );
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document.write( "His bachelorhood lasted  years so he was  \r\n" );
document.write( "years old when his bachelorhood ended.\r\n" );
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document.write( ">>...Five years after his marriage was born a son...<< \r\n" );
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document.write( "His childless marriage lasted 5 years, so he was  \r\n" );
document.write( "years old when his childless marriage ended.\r\n" );
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document.write( ">>...who died...at half his father's {final)age...<<\r\n" );
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document.write( "His life with a live son lasted  years, so \r\n" );
document.write( "he was  years old when his son died.\r\n" );
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document.write( ">>...who died four years before his father,...<<\r\n" );
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document.write( "So he was  years old when he died.\r\n" );
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document.write( "And he was also  years old when he died. So we set \r\n" );
document.write( "these equal:\r\n" );
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document.write( "Combine 5 and 4:\r\n" );
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document.write( "Clear of fractions by multiplying through by \r\n" );
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document.write( "Combine like terms:\r\n" );
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document.write( "Add -75N to both sides:\r\n" );
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document.write( "Divide both sides by 9\r\n" );
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document.write( "Diophantus was 84 years old when he died.\r\n" );
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document.write( "Edwin

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