document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=100024>Question 100024</A>: <I><SPAN STYLE=\"word-break: break-all;\"> in a rational no. twice the numerator is 2 more than the denominator. if 3 is added to each, the numerator or the denominator, the new fraction is 2/3. find the original no.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #72849 by </B><A HREF=/tutors/aboutme.mpl?userid=ptaylor><B>ptaylor(2198)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ptaylor><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=ptaylor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=72849\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x=the numerator<BR>\n" );
document.write( "And let y=the denominator\r<BR>\n" );
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document.write( "Now we are told that:\r<BR>\n" );
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document.write( "2x=y+2-----------------------eq1<BR>\n" );
document.write( "and<BR>\n" );
document.write( "(x+3)/(y+3)=2/3-------------------eq2\r<BR>\n" );
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document.write( "multiply each term in eq2 by 3(y+3) to get rid of fractions and we get:\r<BR>\n" );
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document.write( "3(x+3)=2(y+3)  get rid of parens<BR>\n" );
document.write( "3x+9=2y+6  subtract 9 from both sides:\r<BR>\n" );
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document.write( "3x=2y-3---------------------eq2<BR>\n" );
document.write( "multiply eq1 by 2 and subtract it from eq2:<BR>\n" );
document.write( "eq2-2*(eq1)=\r<BR>\n" );
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document.write( " 3x=2y-3<BR>\n" );
document.write( "-4x=-2y-4\r<BR>\n" );
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document.write( "-x=-7 or\r<BR>\n" );
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document.write( "x=7-----------------numerator<BR>\n" );
document.write( "substitute x=7 into eq1\r<BR>\n" );
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document.write( "2*7=y+2  subtract 2 from both sides\r<BR>\n" );
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document.write( "14-2=y\r<BR>\n" );
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document.write( "y=12-----------denominator\r<BR>\n" );
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document.write( "CK\r<BR>\n" );
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document.write( "(7+3)/(12+3)=2/3\r<BR>\n" );
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document.write( "10/15=2/3<BR>\n" );
document.write( "2/3=2/3\r<BR>\n" );
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document.write( "also<BR>\n" );
document.write( "2*7=12+2<BR>\n" );
document.write( "14=14\r<BR>\n" );
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document.write( "Hope this helps-----ptaylor\r<BR>\n" );
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document.write( " </SPAN>\n" );
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