document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=57369>Question 57369</A>: <I><SPAN STYLE=\"word-break: break-all;\"> One number is 5 times another. If the sum of their reciprocal is 6/35, find the two numbers. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #39112 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=39112\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let the two numbers be a and b.\r<BR>\n" );
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document.write( "a = 5b  One number is 5 times another.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fa+%2B+1%2Fb+=+6%2F35 ALIGN=MIDDLE  ALT=\"1%2Fa+%2B+1%2Fb+=+6%2F35\"   DISABLED_style= \"max-width:90%; height:auto;\" > The sum of their reciprocals is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2F35 ALIGN=MIDDLE  ALT=\"6%2F35\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplifying this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2Bb%29%2Fab+=+6%2F35 ALIGN=MIDDLE  ALT=\"%28a%2Bb%29%2Fab+=+6%2F35\"   DISABLED_style= \"max-width:90%; height:auto;\" > Cross-multiply.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=35a+%2B+35b+=+6ab ALIGN=MIDDLE  ALT=\"35a+%2B+35b+=+6ab\"   DISABLED_style= \"max-width:90%; height:auto;\" > Substitute a = 5b.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=175b+%2B+35b+=+30b%5E2 ALIGN=MIDDLE  ALT=\"175b+%2B+35b+=+30b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=210b+=+30b%5E2 ALIGN=MIDDLE  ALT=\"210b+=+30b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30b%5E2+-+210b+=+0 ALIGN=MIDDLE  ALT=\"30b%5E2+-+210b+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor out a b.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%2830b+-+210%29+=+0 ALIGN=MIDDLE  ALT=\"b%2830b+-+210%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Apply the  zero product principle.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+0 ALIGN=MIDDLE  ALT=\"b+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and/or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30b+-+210+=+0 ALIGN=MIDDLE  ALT=\"30b+-+210+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+0 ALIGN=MIDDLE  ALT=\"b+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Discard this solution as not meaningful.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30b+-+210+=+0 ALIGN=MIDDLE  ALT=\"30b+-+210+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add 210 to both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30b+=+210 ALIGN=MIDDLE  ALT=\"30b+=+210\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 30.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+7 ALIGN=MIDDLE  ALT=\"b+=+7\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+5b ALIGN=MIDDLE  ALT=\"a+=+5b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+35 ALIGN=MIDDLE  ALT=\"a+=+35\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The two numbers are:<BR>\n" );
document.write( "7 and 35\r<BR>\n" );
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document.write( "Check:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F7+%2B+1%2F35+=+5%2F35+%2B+1%2F35 ALIGN=MIDDLE  ALT=\"1%2F7+%2B+1%2F35+=+5%2F35+%2B+1%2F35\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2F35 ALIGN=MIDDLE  ALT=\"6%2F35\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=35+=+5%287%29 ALIGN=MIDDLE  ALT=\"35+=+5%287%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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