document.write( "Question 83824: Here you see the tomb of Diophantis 1/6 of his life god granted him youth. After 1/12 more his cheeks were bearded. After an additional 1/7 he kindled the light of marriage. In the 5th year of marriage he fathered a son. Alas, the sons life span was only 1/2 that of his fathers, who grieved during the remaining 4 years of his life. By the device of Alegbra, tell the extent of both Diaphantis and his sons life. \n" ); document.write( "

Algebra.Com's Answer #60294 by Edwin McCravy(20056) $\"\"$ $\"About$

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Here you see the tomb of Diophantis 1/6 of his life god granted him youth. After 1/12 more his cheeks were bearded. After an additional 1/7 he kindled the light of marriage. In the 5th year of marriage he fathered a son. Alas, the sons life span was only 1/2 that of his fathers, who grieved during the remaining 4 years of his life. By the device of Alegbra, tell the extent of both Diaphantis and his sons life.
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document.write( "Let L = Diophantis' life span (age at death).\r\n" );
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document.write( "...1/6 of his life god granted him youth...\r\n" );
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document.write( "L = his youth years\r\n" );
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document.write( "...After 1/12 more his cheeks were bearded...\r\n" );
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document.write( "So his cheeks bearded at age L + L\r\n" );
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document.write( "...After an additional 1/7 he kindled the light of marriage...\r\n" );
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document.write( "So he married at age L + L + L\r\n" );
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document.write( "...In the 5th year of marriage he fathered a son...\r\n" );
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document.write( "So he fathered a son at age L + L + L + 5\r\n" );
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document.write( "...Alas, the son's life span was only 1/2 that of his fathers...\r\n" );
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document.write( "So when his son died his (Diophantis') age was L + L + L + 5 + L\r\n" );
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document.write( "...who grieved during the remaining 4 years of his life...\r\n" );
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document.write( "So Diophantis died at age: L + L + L + 5 + L + 4\r\n" );
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document.write( "And that must equal to his total lifespan L:\r\n" );
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document.write( "L + L + L + 5 + L + 4 = L\r\n" );
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document.write( "Multiply by the LCD of 84\r\n" );
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document.write( "84L + 84L + 84L + 84·5 + 84L + 84·4 = 84L\r\n" );
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document.write( "14L + 7L + 12L + 420 + 42L + 336 = 84L\r\n" );
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document.write( "75L + 756 = 84L\r\n" );
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document.write( "75L - 84L = -756\r\n" );
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document.write( "       -9L = -756\r\n" );
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document.write( "         L = 84.\r\n" );
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document.write( "So Diophantis lived to be 84.\r\n" );
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document.write( "...1/6 of his life god granted him youth...\r\n" );
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document.write( "L = = 14 his youth years\r\n" );
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document.write( "...After 1/12 more his cheeks were bearded...\r\n" );
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document.write( "So his cheeks bearded at age L + L = 21\r\n" );
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document.write( "...After an additional 1/7 he kindled the light of marriage...\r\n" );
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document.write( "So he married at age L + L + L = 33\r\n" );
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document.write( "...In the 5th year of marriage he fathered a son...\r\n" );
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document.write( "So he fathered a son at age L + L + L + 5\r\n" );
document.write( "= 38\r\n" );
document.write( "...Alas, the son's life span was only 1/2 that of his fathers...\r\n" );
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document.write( "So when his son died his (Diophantis') age was L + L + L + 5 + L = 80\r\n" );
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document.write( "Which means his son only lived to be 42.\r\n" );
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document.write( "Then Diophantis died 4 years later at age 84.\r\n" );
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document.write( "Edwin

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