document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=633036>Question 633036</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The age of the father of two children is twice that of the elder one added to four times that of the younger one. If the geometric mean of the ages of the two children is 4&#8730;3 and their harmonic mean is 6, then what is the father's age? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #398610 by </B><A HREF=/tutors/aboutme.mpl?userid=mananth><B>mananth(16946)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mananth><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=mananth><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=398610\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let the childrens' age be x & y  , x >y<BR>\n" );
document.write( "Father's age 2x+4y\r<BR>\n" );
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document.write( "xy= 48\r<BR>\n" );
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document.write( "Harmonic mean <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2F%281%2Fx%2B1%2Fy%29%29 ALIGN=MIDDLE  ALT=\"%282%2F%281%2Fx%2B1%2Fy%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2F%28%28x%2By%29%2Fxy%29%29%29 ALIGN=MIDDLE  ALT=\"%282%2F%28%28x%2By%29%2Fxy%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=6\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2xy%2F%28x%2By%29+=6 ALIGN=MIDDLE  ALT=\"2xy%2F%28x%2By%29+=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "xy = 48\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A48%2F%28x%2By%29 ALIGN=MIDDLE  ALT=\"2%2A48%2F%28x%2By%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >= 6\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By=+96%2F6 ALIGN=MIDDLE  ALT=\"x%2By=+96%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "x+y = 16<BR>\n" );
document.write( "xy = 48\r<BR>\n" );
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document.write( "x=48/y\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=48%2Fy+%2B+y+=+16 ALIGN=MIDDLE  ALT=\"48%2Fy+%2B+y+=+16\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "multiply equation by y<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=48%2By%5E2=16y ALIGN=MIDDLE  ALT=\"48%2By%5E2=16y\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2-16y%2B48=0 ALIGN=MIDDLE  ALT=\"y%5E2-16y%2B48=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2-8x-6x%2B48=0 ALIGN=MIDDLE  ALT=\"y%5E2-8x-6x%2B48=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%28y-8%29-6%28y-8%29=0 ALIGN=MIDDLE  ALT=\"y%28y-8%29-6%28y-8%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "(y-8)(y-6)=0\r<BR>\n" );
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document.write( "y= 8 OR 6\r<BR>\n" );
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document.write( "xy = 48 <BR>\n" );
document.write( "therefore x=8 \r<BR>\n" );
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document.write( "The sons' ages are 8 & 6\r<BR>\n" );
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document.write( "Father's age 2x+4y  -> 2*8+4*6\r<BR>\n" );
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document.write( "=40 years\r<BR>\n" );
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document.write( "m.ananth@hotmail.ca\r<BR>\n" );
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document.write( " </SPAN>\n" );
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