document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=666968>Question 666968</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The denominator of a fraction is 5 more than the numerator. If both the numerator and denominator are decreased by 2, the resulting fraction is equivalent to 7/12. Find the fraction. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #415230 by </B><A HREF=/tutors/aboutme.mpl?userid=ReadingBoosters><B>ReadingBoosters(3246)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ReadingBoosters><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=415230\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Establish variables<BR>\n" );
document.write( "x = numerator<BR>\n" );
document.write( "y = denominator<BR>\n" );
document.write( "...<BR>\n" );
document.write( "Given<BR>\n" );
document.write( "y = x+5<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-2%29%2F%28y-2%29+=+7%2F12 ALIGN=MIDDLE  ALT=\"%28x-2%29%2F%28y-2%29+=+7%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "...<BR>\n" );
document.write( "Substitute y into the second equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-2%29%2F%28%28x%2B5%29-2%29+=+7%2F12 ALIGN=MIDDLE  ALT=\"%28x-2%29%2F%28%28x%2B5%29-2%29+=+7%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "...<BR>\n" );
document.write( "Cross multiply<BR>\n" );
document.write( "12(x-2) = 7((x+5)-2)<BR>\n" );
document.write( "12x - 24 = 7x + 35 - 14<BR>\n" );
document.write( "...<BR>\n" );
document.write( "Combine like terms<BR>\n" );
document.write( "12x - 7x = 35 - 14 + 24<BR>\n" );
document.write( "5x = 45<BR>\n" );
document.write( "x = 9<BR>\n" );
document.write( "...<BR>\n" );
document.write( "y = x+5 = 9+5 = 14<BR>\n" );
document.write( "...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%289%2F14%29 ALIGN=MIDDLE  ALT=\"highlight_green%289%2F14%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Which was the long way of seeing that <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%287%2B2%29%2F%2812%2B2%29+=+9%2F14 ALIGN=MIDDLE  ALT=\"%287%2B2%29%2F%2812%2B2%29+=+9%2F14\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".....................<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );