document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=739464>Question 739464</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The value of a fraction is 2/3. If the numerator is increased by 14 and the denominator is decreased by 9 the value of the resulting fraction will be the reciprocal of the value of the original fraction. What is the original fraction? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #451128 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39620)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=451128\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You just stated that the original fraction is 2/3 and you ask what is this fraction.  It's the same: 2/3.  \r<BR>\n" );
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document.write( "Did you mean that the ratio of two variables is 2/3, and then according to the description, find those two numbers?  That would be worded a little differently.\r<BR>\n" );
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document.write( "Let numerator be n<BR>\n" );
document.write( "Let denominator be d.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%2Fd+=+2%2F3 ALIGN=MIDDLE  ALT=\"n%2Fd+=+2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "The longer part of the description gives <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28n%2B14%29%2F%28d-9%29=d%2Fn ALIGN=MIDDLE  ALT=\"%28n%2B14%29%2F%28d-9%29=d%2Fn\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Working with the longer equation,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+n%28n%2B14%29=d%28d-9%29 ALIGN=MIDDLE  ALT=\"+n%28n%2B14%29=d%28d-9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5E2%2B14n=d%5E2-9d ALIGN=MIDDLE  ALT=\"n%5E2%2B14n=d%5E2-9d\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Using the 2/3 equation, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=2d%2F3 ALIGN=MIDDLE  ALT=\"n=2d%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so try substituting:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5E2-9d=4d%5E2%2F9%2B14%2A2d%2F3 ALIGN=MIDDLE  ALT=\"d%5E2-9d=4d%5E2%2F9%2B14%2A2d%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiply both sides by 9<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9d%5E2-81d=4d%5E2%2B84d ALIGN=MIDDLE  ALT=\"9d%5E2-81d=4d%5E2%2B84d\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5d%5E2-165d=0 ALIGN=MIDDLE  ALT=\"5d%5E2-165d=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5E2-33d=0 ALIGN=MIDDLE  ALT=\"d%5E2-33d=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%28d-33%29=0 ALIGN=MIDDLE  ALT=\"d%28d-33%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "... <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28d=33%29 ALIGN=MIDDLE  ALT=\"highlight%28d=33%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "meaning <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28n=22%29 ALIGN=MIDDLE  ALT=\"highlight%28n=22%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( " </SPAN>\n" );
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