document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1101288>Question 1101288</A>: <I><SPAN STYLE=\"word-break: break-all;\"> One positive number is 10 less than another positive number. If the reciprocal of the smaller number is added to three times the reciprocal of the larger number, the sum is 1/4. 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 #715917 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=715917\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> One positive number is 10 less than another positive number.<BR>\n" );
document.write( "a = b- 10<BR>\n" );
document.write( " If the reciprocal of the smaller number is added to three times the reciprocal of the larger number, the sum is 1/4.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fa ALIGN=MIDDLE  ALT=\"1%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Fb ALIGN=MIDDLE  ALT=\"3%2Fb\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F4 ALIGN=MIDDLE  ALT=\"1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "multiply by 4ab, cancel the denominators<BR>\n" );
document.write( "4b + 12a = ab<BR>\n" );
document.write( "replace a with (b-10)<BR>\n" );
document.write( "4b + 12(b-10) = b(b-10)<BR>\n" );
document.write( "4b + 12b - 120 = b^2 - 10b <BR>\n" );
document.write( "16b - 120 = b^2 - 10b<BR>\n" );
document.write( "combine to form a quadratic equation on the right<BR>\n" );
document.write( "0 = b^2- 10b - 16b + 120<BR>\n" );
document.write( "b^2 - 26b + 120 = 0<BR>\n" );
document.write( "factors to<BR>\n" );
document.write( "(b-6)(b-20) = 0<BR>\n" );
document.write( "two solutions<BR>\n" );
document.write( "b = 6, not possible, a has to be positive<BR>\n" );
document.write( "b = 20, this is our solution<BR>\n" );
document.write( "then<BR>\n" );
document.write( "a = 20 - 10<BR>\n" );
document.write( "a = 10<BR>\n" );
document.write( " Find the two numbers: 10 & 20<BR>\n" );
document.write( ":<BR>\n" );
document.write( ":<BR>\n" );
document.write( ":<BR>\n" );
document.write( "see if that checks out<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F10 ALIGN=MIDDLE  ALT=\"1%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F20 ALIGN=MIDDLE  ALT=\"3%2F20\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F4 ALIGN=MIDDLE  ALT=\"1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F20 ALIGN=MIDDLE  ALT=\"2%2F20\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F20 ALIGN=MIDDLE  ALT=\"3%2F20\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F4 ALIGN=MIDDLE  ALT=\"1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F20 ALIGN=MIDDLE  ALT=\"5%2F20\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F4 ALIGN=MIDDLE  ALT=\"1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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