document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=738312>Question 738312</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 12.	The sum of numerator and denominator of a fraction is 8. I 3 is added to both numerator and denominator, the fraction becomes ¾. 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 #450808 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=450808\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> THE FIFTH-GRADER WAY:<BR>\n" );
document.write( "after adding 3 to numerator and denominator the new fraction is <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F4=6%2F8=9%2F12=12%2F16=15%2F20 ALIGN=MIDDLE  ALT=\"3%2F4=6%2F8=9%2F12=12%2F16=15%2F20\"   DISABLED_style= \"max-width:90%; height:auto;\" >= .....<BR>\n" );
document.write( "If the new fraction was <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;\" >, the original fraction would have been <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%2F1 ALIGN=MIDDLE  ALT=\"0%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" >. That is just zero, which is not much of a fraction, and even if you say that the numerator is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the denominator is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the sum of numerator plus denominator would be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%2B1=1 ALIGN=MIDDLE  ALT=\"0%2B1=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which is not <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8 ALIGN=MIDDLE  ALT=\"8\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "If the new fraction was <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2F8 ALIGN=MIDDLE  ALT=\"6%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the original fraction would have been <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286-3%29%2F%288-3%29=3%2F5 ALIGN=MIDDLE  ALT=\"%286-3%29%2F%288-3%29=3%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and that is a solution to the problem, because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2B5=8 ALIGN=MIDDLE  ALT=\"3%2B5=8\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "since the wording suggests that there is one solution, no need to try <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2F12 ALIGN=MIDDLE  ALT=\"9%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2F16 ALIGN=MIDDLE  ALT=\"12%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" >, etc,  but it is clear that those would make an original fraction with a sum of numerator plus denominator greater than <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8 ALIGN=MIDDLE  ALT=\"8\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( " <BR>\n" );
document.write( "THE ALGEBRA WAY:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Fy ALIGN=MIDDLE  ALT=\"x%2Fy\"   DISABLED_style= \"max-width:90%; height:auto;\" >= the fraction<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >= the numerator<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" >= the denominator<BR>\n" );
document.write( " <BR>\n" );
document.write( "The sum of numerator and denominator of a fraction is 8 translates into<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By=8 ALIGN=MIDDLE  ALT=\"x%2By=8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "If 3 is added to both numerator and denominator, 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;\" > translates into<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B3%29%2F%28y%2B3%29=3%2F4%7D%7D+--%3E+%7B%7B%7B4%2A%28x%2B3%29=3%2A%28y%2B3%29 ALIGN=MIDDLE  ALT=\"%28x%2B3%29%2F%28y%2B3%29=3%2F4%7D%7D+--%3E+%7B%7B%7B4%2A%28x%2B3%29=3%2A%28y%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%2B12=3y%2B9 ALIGN=MIDDLE  ALT=\"4x%2B12=3y%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x-3y=9-12 ALIGN=MIDDLE  ALT=\"4x-3y=9-12\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x-3y=-3 ALIGN=MIDDLE  ALT=\"4x-3y=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "Now we have to solve the system <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28x%2By=8%2C4x-3y=-3%29 ALIGN=MIDDLE  ALT=\"system%28x%2By=8%2C4x-3y=-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "We solve it any way we can to find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=3%29 ALIGN=MIDDLE  ALT=\"highlight%28x=3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y=5%29 ALIGN=MIDDLE  ALT=\"highlight%28y=5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "SUBSTITUTION:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By=8 ALIGN=MIDDLE  ALT=\"x%2By=8\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=8-y ALIGN=MIDDLE  ALT=\"x=8-y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28x=8-y%2C4x-3y=-3%29 ALIGN=MIDDLE  ALT=\"system%28x=8-y%2C4x-3y=-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2A%288-y%29-3y=-3 ALIGN=MIDDLE  ALT=\"4%2A%288-y%29-3y=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=32-4y-3y=-3 ALIGN=MIDDLE  ALT=\"32-4y-3y=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=32-7y=-3 ALIGN=MIDDLE  ALT=\"32-7y=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=32%2B3=7y ALIGN=MIDDLE  ALT=\"32%2B3=7y\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7y=35 ALIGN=MIDDLE  ALT=\"7y=35\"   DISABLED_style= \"max-width:90%; height:auto;\" > --><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=35%2F7 ALIGN=MIDDLE  ALT=\"y=35%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y=5%29 ALIGN=MIDDLE  ALT=\"highlight%28y=5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28y=5%2Cx=8-y%29 ALIGN=MIDDLE  ALT=\"system%28y=5%2Cx=8-y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=8-5 ALIGN=MIDDLE  ALT=\"x=8-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=3%29 ALIGN=MIDDLE  ALT=\"highlight%28x=3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );