document.write( "Question 194190: \"Diophantus passed 1/6 of his life in childhood, 1/12 in youth and 1/7 more as a bachelor. Five years after his marriage, was born a son who died 4 years before his father, at 1/2 his father's final age.\" How old was Diophantus when he died? \n" ); document.write( "

Algebra.Com's Answer #145792 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

You can put this solution on YOUR website!
\"Diophantus passed 1/6 of his life in childhood, 1/12 in youth and 1/7 more
\n" ); document.write( " as a bachelor. Five years after his marriage, was born a son who died 4 years
\n" ); document.write( " before his father, at 1/2 his father's final age.\" How old was Diophantus when he died?
\n" ); document.write( ":
\n" ); document.write( "Let x = his final age
\n" ); document.write( ":
\n" ); document.write( "a lengthy but simple equation
\n" ); document.write( ":
\n" ); document.write( "Final age = child + youth + bach + marriage + son's age + 4
\n" ); document.write( "x = $\"1%2F6\"$ x + $\"1%2F12\"$ x + $\"1%2F7\"$ x + 5 + $\"1%2F2\"$ x + 4
\n" ); document.write( ":
\n" ); document.write( "Common denominator of 12*7 = 84
\n" ); document.write( "x = $\"14%2F84\"$ x + $\"7%2F84\"$ x + $\"12%2F84\"$ x + 5 + $\"42%2F84\"$ x + 4
\n" ); document.write( ":
\n" ); document.write( "x = $\"75%2F84\"$ x + 9
\n" ); document.write( ":
\n" ); document.write( " $\"84%2F84\"$ x - $\"75%2F84\"$ x = 9
\n" ); document.write( ":
\n" ); document.write( " $\"9%2F84\"$ x = 9
\n" ); document.write( ":
\n" ); document.write( "Multiply both sides by 84
\n" ); document.write( "9x = 84(9)
\n" ); document.write( ":
\n" ); document.write( "x = 84 is his final age
\n" ); document.write( ":
\n" ); document.write( "Check:
\n" ); document.write( "14 + 7 + 12 + 5 + 42 + 4 = 84 \n" ); document.write( "

\n" );