document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=983538>Question 983538</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the ratio of the ages of A:B=6:5, AND THE AGE of each C and D is 9/10 times that Of B . Age of F is less than A but greater then B . The ratio of age of B&E is 2:3 ,also age of A is 3 years less than E .What is the ratio of age of A and F ,if all the pages are in integers ? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #604608 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=604608\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A ALIGN=MIDDLE  ALT=\"A\"   DISABLED_style= \"max-width:90%; height:auto;\" >= age of A,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B ALIGN=MIDDLE  ALT=\"B\"   DISABLED_style= \"max-width:90%; height:auto;\" >= age of B,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C ALIGN=MIDDLE  ALT=\"C\"   DISABLED_style= \"max-width:90%; height:auto;\" >= age of C,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D ALIGN=MIDDLE  ALT=\"D\"   DISABLED_style= \"max-width:90%; height:auto;\" >= age of D,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=E ALIGN=MIDDLE  ALT=\"E\"   DISABLED_style= \"max-width:90%; height:auto;\" >= age of E, and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=F ALIGN=MIDDLE  ALT=\"F\"   DISABLED_style= \"max-width:90%; height:auto;\" >= age of F.<BR>\n" );
document.write( "We can use the ratios to calculate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B ALIGN=MIDDLE  ALT=\"B\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C ALIGN=MIDDLE  ALT=\"C\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D ALIGN=MIDDLE  ALT=\"D\"   DISABLED_style= \"max-width:90%; height:auto;\" > , and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=E ALIGN=MIDDLE  ALT=\"E\"   DISABLED_style= \"max-width:90%; height:auto;\" > in terms of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A ALIGN=MIDDLE  ALT=\"A\"   DISABLED_style= \"max-width:90%; height:auto;\" > :<BR>\n" );
document.write( "The ratio of the ages of A:B=6:5. ---> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%2FB=6%2F5 ALIGN=MIDDLE  ALT=\"A%2FB=6%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5A=6B ALIGN=MIDDLE  ALT=\"5A=6B\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%2F6%29A=B ALIGN=MIDDLE  ALT=\"%285%2F6%29A=B\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The age of each C and D is 9/10 times that Of B. ---> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=D=%289%2F10%29B=%289%2F10%29%285%2F6%29A=%283%2F4%29A ALIGN=MIDDLE  ALT=\"C=D=%289%2F10%29B=%289%2F10%29%285%2F6%29A=%283%2F4%29A\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The ratio of age of B&E is 2:3. ---> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B%2FE=2%2F3 ALIGN=MIDDLE  ALT=\"B%2FE=2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2E=3B ALIGN=MIDDLE  ALT=\"2E=3B\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=E=%283%2F2%29B ALIGN=MIDDLE  ALT=\"E=%283%2F2%29B\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=E=%283%2F2%29%285%2F6%29A=%285%2F4%29A ALIGN=MIDDLE  ALT=\"E=%283%2F2%29%285%2F6%29A=%285%2F4%29A\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "For all those ages to be integers, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A ALIGN=MIDDLE  ALT=\"A\"   DISABLED_style= \"max-width:90%; height:auto;\" > must be a multiple of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6 ALIGN=MIDDLE  ALT=\"6\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "so it must be a multiple of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12 ALIGN=MIDDLE  ALT=\"12\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "We can use \"guess and check\" from here, trying 12, 24, 36, etc as values for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A ALIGN=MIDDLE  ALT=\"A\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "We can also say that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=12N ALIGN=MIDDLE  ALT=\"A=12N\"   DISABLED_style= \"max-width:90%; height:auto;\" > for some whole number <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N ALIGN=MIDDLE  ALT=\"N\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and express everyone's age as a function of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N ALIGN=MIDDLE  ALT=\"N\"   DISABLED_style= \"max-width:90%; height:auto;\" > :<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=12N ALIGN=MIDDLE  ALT=\"A=12N\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B=%285%2F6%29%2812N%29=10N ALIGN=MIDDLE  ALT=\"B=%285%2F6%29%2812N%29=10N\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%2BD%2B%283%2F4%29%2812N%29=9N ALIGN=MIDDLE  ALT=\"C%2BD%2B%283%2F4%29%2812N%29=9N\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=E=%285%2F4%29%2812N%29=15N ALIGN=MIDDLE  ALT=\"E=%285%2F4%29%2812N%29=15N\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The age of A is 3 years less than E. ---> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12N=15N-3 ALIGN=MIDDLE  ALT=\"12N=15N-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15N-12N=3 ALIGN=MIDDLE  ALT=\"15N-12N=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3N=3 ALIGN=MIDDLE  ALT=\"3N=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N=3%2F3 ALIGN=MIDDLE  ALT=\"N=3%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N=1 ALIGN=MIDDLE  ALT=\"N=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "So,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=12N=12%2A1=12 ALIGN=MIDDLE  ALT=\"A=12N=12%2A1=12\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B=10N=10%2A1=10 ALIGN=MIDDLE  ALT=\"B=10N=10%2A1=10\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Since the age of F is less than A but greater than B, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=F=11 ALIGN=MIDDLE  ALT=\"F=11\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and the rati we need is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%2FF=highlight%2812%2F11%29 ALIGN=MIDDLE  ALT=\"A%2FF=highlight%2812%2F11%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > . </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );