document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=630693>Question 630693</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Diaphanous was a famous Greek mathematician who lived and worked in Alexandria, Egypt, probably in the third century C.E. When he died, someone described his life in this puzzle. He was a boy for 1/6 of his life. After 1/12 more, he acquired a beard. After another 1/7, he married. In the fifth year after his marriage, his son was born. The son lived half as many years as his father. Diaphanous died 4 years after his son. How old was Diaphanous when he died? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #397184 by </B><A HREF=/tutors/aboutme.mpl?userid=MathTherapy><B>MathTherapy(10552)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathTherapy><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=MathTherapy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=397184\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Diaphanous was a famous Greek mathematician who lived and worked in Alexandria, Egypt, probably in the third century C.E. When he died, someone described his life in this puzzle. He was a boy for 1/6 of his life. After 1/12 more, he acquired a beard. After another 1/7, he married. In the fifth year after his marriage, his son was born. The son lived half as many years as his father. Diaphanous died 4 years after his son. How old was Diaphanous when he died?\r<BR>\n" );
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document.write( "Let Diaphanous’ age when he died be D<BR>\n" );
document.write( "He was a boy for <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;\" > of D, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%2F6 ALIGN=MIDDLE  ALT=\"D%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Since after <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;\" > more years, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%2F12 ALIGN=MIDDLE  ALT=\"D%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" >, he acquired a beard, then he acquired a beard at age: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%2F6+%2B+D%2F12 ALIGN=MIDDLE  ALT=\"D%2F6+%2B+D%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282D+%2B+D%29%2F12 ALIGN=MIDDLE  ALT=\"%282D+%2B+D%29%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3D%2F12 ALIGN=MIDDLE  ALT=\"3D%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%2F4 ALIGN=MIDDLE  ALT=\"D%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Since after <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;\" > more years, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%2F7 ALIGN=MIDDLE  ALT=\"D%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" >, he got married, then he got married at age: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%2F4+%2B+D%2F7 ALIGN=MIDDLE  ALT=\"D%2F4+%2B+D%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%287D+%2B+4D%29%2F28 ALIGN=MIDDLE  ALT=\"%287D+%2B+4D%29%2F28\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11D%2F28 ALIGN=MIDDLE  ALT=\"11D%2F28\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Since his son was born 5 years after he got married, then his son was born when he was: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11D%2F28+%2B+5 ALIGN=MIDDLE  ALT=\"11D%2F28+%2B+5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Since son lived for ½D, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%2F2 ALIGN=MIDDLE  ALT=\"D%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then Diaphanous was <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11D%2F28+%2B+5+%2B+D%2F2 ALIGN=MIDDLE  ALT=\"11D%2F28+%2B+5+%2B+D%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > when his son died<BR>\n" );
document.write( "Since he died 4 years after his son’s death, he died at age <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11D%2F28+%2B+5+%2B+D%2F2+%2B+4 ALIGN=MIDDLE  ALT=\"11D%2F28+%2B+5+%2B+D%2F2+%2B+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11D%2F28+%2B+D%2F2+%2B+9 ALIGN=MIDDLE  ALT=\"11D%2F28+%2B+D%2F2+%2B+9\"   DISABLED_style= \"max-width:90%; height:auto;\" >. The age that he died is also D<BR>\n" );
document.write( "Therefore, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11D%2F28+%2B+D%2F2+%2B+9+=+D ALIGN=MIDDLE  ALT=\"11D%2F28+%2B+D%2F2+%2B+9+=+D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "11D + 14D + 252 = 28D ------ Multilpying by LCD, 28<BR>\n" );
document.write( "11D + 14D – 28D = - 252 <BR>\n" );
document.write( "- 3D = - 252<BR>\n" );
document.write( "D, or age that Diaphanous died at was: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-+252%29%2F-+3 ALIGN=MIDDLE  ALT=\"%28-+252%29%2F-+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%2884%29 ALIGN=MIDDLE  ALT=\"highlight_green%2884%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Check<BR>\n" );
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document.write( "Lived for 84 years<BR>\n" );
document.write( "Boy for <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;\" > of 84, or 14 years<BR>\n" );
document.write( "After <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;\" > of 84, or 7 years, he acquired a beard. Acquired beard @ age 21 (14 + 7)<BR>\n" );
document.write( "After <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;\" > of 84, or 12 years, he got married. Got married @ age 33 (21 + 12)<BR>\n" );
document.write( "After 5 years of marriage, his son was born. Son was born @ age 38 (33 + 5)<BR>\n" );
document.write( "Son lived for ½ of 84, or for 42 years. Age at son’s death = 80 (38 + 42)<BR>\n" );
document.write( "He died 4 years after son’s death. Died at age 84 (80 + 4)\r<BR>\n" );
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document.write( "Send comments and “thank-yous” to “D” at  MathMadEzy@aol.com </SPAN>\n" );
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