document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1000680>Question 1000680</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a positive integer is 5 less than another if the reciprocal of the smaller integer is subtracted from 3 times the reciprocals of the larger than the result is 1/12 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #618156 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=618156\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a positive integer is 5 less than another<BR>\n" );
document.write( "a = b - 5<BR>\n" );
document.write( " if the reciprocal of the smaller integer is subtracted from 3 times the reciprocals of the larger than the result is 1/12<BR>\n" );
document.write( "<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%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=1%2F12 ALIGN=MIDDLE  ALT=\"1%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Replace a with (b-5) from the 1st statement<BR>\n" );
document.write( "<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%2F%28%28b-5%29%29 ALIGN=MIDDLE  ALT=\"1%2F%28%28b-5%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <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;\" ><BR>\n" );
document.write( "Multiply equation by 12b(b-5), cancel the denominators<BR>\n" );
document.write( "12(3)(b-5) - 12b = b(b-5)<BR>\n" );
document.write( "36a - 180 - 12b = b^2 - 5b<BR>\n" );
document.write( "24a - 180 = b^2 - 5b<BR>\n" );
document.write( "Form a quadratic equation on the right<BR>\n" );
document.write( "0 = b^2 - 5b - 24a + 180<BR>\n" );
document.write( "b^2 - 29b + 180 = 0<BR>\n" );
document.write( "Factors to<BR>\n" );
document.write( "(b-20)(b-9) = 0<BR>\n" );
document.write( "two solutions<BR>\n" );
document.write( "b = 20, then a = 15<BR>\n" );
document.write( "b = 9, then a = 4<BR>\n" );
document.write( ":<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Check the first pair in the original equation<BR>\n" );
document.write( "<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%2F15 ALIGN=MIDDLE  ALT=\"1%2F15\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <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;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2F60 ALIGN=MIDDLE  ALT=\"9%2F60\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F60 ALIGN=MIDDLE  ALT=\"4%2F60\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F60 ALIGN=MIDDLE  ALT=\"5%2F60\"   DISABLED_style= \"max-width:90%; height:auto;\" > Which is 1/12<BR>\n" );
document.write( ":<BR>\n" );
document.write( "You can check the 2nd pair in the same equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F9 ALIGN=MIDDLE  ALT=\"3%2F9\"   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;\" > = <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;\" >\r<BR>\n" );
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document.write( "  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );