document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=984487>Question 984487</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The ratio of numerator to denominator is 2 to 3.  If both are increased by 2, the fraction becomes 3/4. What is original fraction?  Which of following systems can be used to solve? \r<BR>\n" );
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document.write( "N+4=3 and d+5=4<BR>\n" );
document.write( "or<BR>\n" );
document.write( "3n-2d=0 and 4n+2=3d+2<BR>\n" );
document.write( "or <BR>\n" );
document.write( "3n=2d and 4n+8=3d+6\r<BR>\n" );
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document.write( "How do you figure this out?  Lost! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #605273 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=605273\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let's numerator be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" > and denominator <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d ALIGN=MIDDLE  ALT=\"d\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "given: the ratio of numerator to denominator is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so, we have <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;\" >.......eq.1\r<BR>\n" );
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document.write( "if both are increased by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the fraction becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F4 ALIGN=MIDDLE  ALT=\"3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28n%2B2%29%2F%28d%2B2%29=3%2F4 ALIGN=MIDDLE  ALT=\"%28n%2B2%29%2F%28d%2B2%29=3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >.......eq.2\r<BR>\n" );
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document.write( "to figure out hat is original fraction, solve this system:\r<BR>\n" );
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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;\" >.......eq.1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28n%2B2%29%2F%28d%2B2%29=3%2F4 ALIGN=MIDDLE  ALT=\"%28n%2B2%29%2F%28d%2B2%29=3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >.......eq.2<BR>\n" );
document.write( "----------------------------------------\r<BR>\n" );
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document.write( "start with <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;\" >.......eq.1 and solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=%282%2F3%29d ALIGN=MIDDLE  ALT=\"n=%282%2F3%29d\"   DISABLED_style= \"max-width:90%; height:auto;\" >....substitute it in eq.2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%282%2F3%29d%2B2%29%2F%28d%2B2%29=3%2F4 ALIGN=MIDDLE  ALT=\"%28%282%2F3%29d%2B2%29%2F%28d%2B2%29=3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >.......eq.2 and solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d ALIGN=MIDDLE  ALT=\"d\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%282%2F3%29d%2B2%29=%283%2F4%29%28d%2B2%29 ALIGN=MIDDLE  ALT=\"%28%282%2F3%29d%2B2%29=%283%2F4%29%28d%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2d%2F3%2B6%2F3=3d%2F4%2B6%2F4 ALIGN=MIDDLE  ALT=\"2d%2F3%2B6%2F3=3d%2F4%2B6%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >......both sides multiply by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12 ALIGN=MIDDLE  ALT=\"12\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%282d%2F3%29%2B12%286%2F3%29=12%283d%2F4%29%2B12%286%2F4%29 ALIGN=MIDDLE  ALT=\"12%282d%2F3%29%2B12%286%2F3%29=12%283d%2F4%29%2B12%286%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >....simplify\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cross%2812%294%282d%2Fcross%283%29%29%2Bcross%2812%294%286%2Fcross%283%29%29=cross%2812%293%283d%2Fcross%284%29%29%2Bcross%2812%293%286%2Fcross%284%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2A2d%2B4%2A6=3%2A3d%2B3%2A6 ALIGN=MIDDLE  ALT=\"4%2A2d%2B4%2A6=3%2A3d%2B3%2A6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8d%2B24=9d%2B18 ALIGN=MIDDLE  ALT=\"8d%2B24=9d%2B18\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24-18=9d-8d ALIGN=MIDDLE  ALT=\"24-18=9d-8d\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28d=6%29 ALIGN=MIDDLE  ALT=\"highlight%28d=6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "go back to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=%282%2F3%29d ALIGN=MIDDLE  ALT=\"n=%282%2F3%29d\"   DISABLED_style= \"max-width:90%; height:auto;\" >,substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%29 ALIGN=MIDDLE  ALT=\"6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d ALIGN=MIDDLE  ALT=\"d\"   DISABLED_style= \"max-width:90%; height:auto;\" > and solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=%282%2F3%296 ALIGN=MIDDLE  ALT=\"n=%282%2F3%296\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=%282%2Fcross%283%29%29cross%286%292 ALIGN=MIDDLE  ALT=\"n=%282%2Fcross%283%29%29cross%286%292\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=2%2A2 ALIGN=MIDDLE  ALT=\"n=2%2A2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28n=4%29 ALIGN=MIDDLE  ALT=\"highlight%28n=4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so, the numerator is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=4 ALIGN=MIDDLE  ALT=\"n=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and denominator is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=6 ALIGN=MIDDLE  ALT=\"d=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "original fraction is: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%284%2F6%29 ALIGN=MIDDLE  ALT=\"highlight%284%2F6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "check:\r<BR>\n" );
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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;\" >.......eq.1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F6=2%2F3 ALIGN=MIDDLE  ALT=\"4%2F6=2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cross%284%292%2Fcross%286%293=2%2F3 ALIGN=MIDDLE  ALT=\"cross%284%292%2Fcross%286%293=2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F3=2%2F3 ALIGN=MIDDLE  ALT=\"2%2F3=2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >  \r<BR>\n" );
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document.write( "and \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28n%2B2%29%2F%28d%2B2%29=3%2F4 ALIGN=MIDDLE  ALT=\"%28n%2B2%29%2F%28d%2B2%29=3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >.......eq.2<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%2B2%29%2F%286%2B2%29=3%2F4 ALIGN=MIDDLE  ALT=\"%284%2B2%29%2F%286%2B2%29=3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2F8=3%2F4 ALIGN=MIDDLE  ALT=\"6%2F8=3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cross%286%293%2Fcross%288%294=3%2F4 ALIGN=MIDDLE  ALT=\"cross%286%293%2Fcross%288%294=3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F4=3%2F4 ALIGN=MIDDLE  ALT=\"3%2F4=3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );