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 #605274 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=605274\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x/y=2/3<BR>\n" );
document.write( "(x+2)/(y+2)=3/4<BR>\n" );
document.write( "cross-multiply both<BR>\n" );
document.write( "3x=2y; 3x-2y=0<BR>\n" );
document.write( "4x+8=3y+6<BR>\n" );
document.write( "4x-3y=-2<BR>\n" );
document.write( ";;<BR>\n" );
document.write( "Multiply the first equation by 4 and the second equation by (-3) and add it to the first<BR>\n" );
document.write( "12-8y=0<BR>\n" );
document.write( "-12x+9y= 6<BR>\n" );
document.write( "y=6<BR>\n" );
document.write( "x=4<BR>\n" );
document.write( "(x+2)=6<BR>\n" );
document.write( "(y+2)=8; 6/8=3/4<BR>\n" );
document.write( ";<BR>\n" );
document.write( "3n-2d=0<BR>\n" );
document.write( "4n-3d=0, rearranging<BR>\n" );
document.write( "multiply top by 3 and bottom by (-2)<BR>\n" );
document.write( "9n-6d=0<BR>\n" );
document.write( "-8n+6d=0<BR>\n" );
document.write( "n=0<BR>\n" );
document.write( "d=0<BR>\n" );
document.write( "Indeed, that is the only way that 4n+2=3d+2<BR>\n" );
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document.write( "3n=2d; 4n-3d=-2, rearranging. Do it by substitution<BR>\n" );
document.write( "n=(2/3)d; 4n=(8/3)d<BR>\n" );
document.write( "(8/3)d-(9/3)d=-2<BR>\n" );
document.write( "(-1/3)d=-2<BR>\n" );
document.write( "d=6, multiplying both sides by (-3)<BR>\n" );
document.write( "n=4 substituting d into the first and solving for 3n<BR>\n" );
document.write( "4(4)+8=3(6)+6<BR>\n" );
document.write( "24=24 check<BR>\n" );
document.write( "- </SPAN>\n" );
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