document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=698704>Question 698704</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If the numerator and denominator of a certain fraction are increased by 1, the value of the fraction is 1/2. if the numerator of the original fraction is left unchanged and the denominator is increased by 3, the value of the fraction is 1/4. Find the original fraction. \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "THANK YOU if you work this one out! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #430987 by </B><A HREF=/tutors/aboutme.mpl?userid=sofiyac><B>sofiyac(983)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=sofiyac><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=sofiyac><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=430987\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let numerator be x and denominator be y, then our fraction is x/y. Now we follow the problem and create equauations<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B1%29%2F%28y%2B1%29=1%2F2 ALIGN=MIDDLE  ALT=\"%28x%2B1%29%2F%28y%2B1%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=x%2F%28y%2B3%29=1%2F4 ALIGN=MIDDLE  ALT=\"x%2F%28y%2B3%29=1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "we multiply each equation across and get<BR>\n" );
document.write( "2(x+1)=y+1 <BR>\n" );
document.write( "4x=y+3<BR>\n" );
document.write( "********simplify first equaiton<BR>\n" );
document.write( "2x+2=y+1<BR>\n" );
document.write( "4x=y+3<BR>\n" );
document.write( "********subtract 2 from each side on the first equation<BR>\n" );
document.write( "2x=y-1<BR>\n" );
document.write( "4x=y+3<BR>\n" );
document.write( "********multiply first equation by -2<BR>\n" );
document.write( "-4x=-2y+2<BR>\n" );
document.write( "4x=y+3<BR>\n" );
document.write( "**********add the two equations<BR>\n" );
document.write( "0=-y+5 add y to each side<BR>\n" );
document.write( "y=5<BR>\n" );
document.write( "now we plug that into any of the equations since they are all true and solve for x, i'll use the 4x=y+3 equation\r<BR>\n" );
document.write( "\n" );
document.write( "4x=5+3<BR>\n" );
document.write( "4x=8 divide each side by 4<BR>\n" );
document.write( "x=2<BR>\n" );
document.write( "so we said original fraction was x/y so 2/5 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );