document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=781909>Question 781909</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Diophantus's youth lasted one sixth of his life.  He grew a beard after one twelfth more.  After one seventh more of his life, he married.  5 years later, he and his wife had a son.  The son lived exactly one half as long as his father, and Diophantus died four years after his son. \r<BR>\n" );
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document.write( "How many years did Diophantus live? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #476155 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=476155\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Diophantus's youth lasted one sixth of his life.<BR>\n" );
document.write( " He grew a beard after one twelfth more.<BR>\n" );
document.write( " After one seventh more of his life, he married.<BR>\n" );
document.write( " 5 years later, he and his wife had a son.<BR>\n" );
document.write( " The son lived exactly one half as long as his father, and Diophantus died four years after his son.\r<BR>\n" );
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document.write( "How many years did Diophantus live?\r<BR>\n" );
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document.write( "Let x = his final age<BR>\n" );
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document.write( "a lengthy but simple equation<BR>\n" );
document.write( "Final age = child + youth + bach + marriage + son's age + 4 <BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F6 ALIGN=MIDDLE  ALT=\"1%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" >x + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F12 ALIGN=MIDDLE  ALT=\"1%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" >x + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F7 ALIGN=MIDDLE  ALT=\"1%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" >x + 5 + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >x + 4 <BR>\n" );
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document.write( "Common denominator of 12*7 = 84<BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14%2F84 ALIGN=MIDDLE  ALT=\"14%2F84\"   DISABLED_style= \"max-width:90%; height:auto;\" >x + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2F84 ALIGN=MIDDLE  ALT=\"7%2F84\"   DISABLED_style= \"max-width:90%; height:auto;\" >x + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2F84 ALIGN=MIDDLE  ALT=\"12%2F84\"   DISABLED_style= \"max-width:90%; height:auto;\" >x + 5 + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=42%2F84 ALIGN=MIDDLE  ALT=\"42%2F84\"   DISABLED_style= \"max-width:90%; height:auto;\" >x + 4<BR>\n" );
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document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=75%2F84 ALIGN=MIDDLE  ALT=\"75%2F84\"   DISABLED_style= \"max-width:90%; height:auto;\" >x + 9<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=84%2F84 ALIGN=MIDDLE  ALT=\"84%2F84\"   DISABLED_style= \"max-width:90%; height:auto;\" >x - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=75%2F84 ALIGN=MIDDLE  ALT=\"75%2F84\"   DISABLED_style= \"max-width:90%; height:auto;\" >x = 9<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2F84 ALIGN=MIDDLE  ALT=\"9%2F84\"   DISABLED_style= \"max-width:90%; height:auto;\" >x = 9<BR>\n" );
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document.write( "x = 9 * <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=84%2F9 ALIGN=MIDDLE  ALT=\"84%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "x = 84 is his final age<BR>\n" );
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document.write( "Check:<BR>\n" );
document.write( "14 + 7 + 12 + 5 + 42 + 4 = 84  </SPAN>\n" );
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