document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=687224>Question 687224</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The ratio of the numerator to the denominator of a certain fraction is five to eight. If five is subtracted from the numerator and four is added to the denominator, the new fraction reduces to one-half. What is the original fraction?\r<BR>\n" );
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document.write( "A mixture contains \r<BR>\n" );
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document.write( "A girl is now \r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #843723 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=843723\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The other tutor showed a valid solution using two variables.<br><BR>\n" );
document.write( "Setting the problem up using a single variable makes solving the problem much easier.<br><BR>\n" );
document.write( "Given the information that the ratio of numerator to denominator is 5:8, let the numerator be 5x and the denominator be 8x.  That is a very common way to set up a problem where the ratio of two numbers is given.<br><BR>\n" );
document.write( "The fraction with 5 subtracted from the numerator and 4 added to the denominator is equivalent to 1/2:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285x-5%29%2F%288x%2B4%29=1%2F2 ALIGN=MIDDLE  ALT=\"%285x-5%29%2F%288x%2B4%29=1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10x-10=8x%2B4 ALIGN=MIDDLE  ALT=\"10x-10=8x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x=14 ALIGN=MIDDLE  ALT=\"2x=14\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=7 ALIGN=MIDDLE  ALT=\"x=7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The original fraction has numerator 5x=35 and denominator 8x=56.<br><BR>\n" );
document.write( "ANSWER: 35/56<br><BR>\n" );
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