document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=204987>Question 204987</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If the numerator of a certain fraction is increased by 5 and the denominator is decreased by 1, the resulting fraction is 8/3.  However, if the numerator of the original fraction is doubled and the denominator is increased by 7, the resulting fraction is 6/11.  Find the original fraction. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #154723 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=154723\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If the numerator of a certain fraction is increased by 5 and the denominator is decreased by 1, the resulting fraction is 8/3. However, if the numerator of the original fraction is doubled and the denominator is increased by 7, the resulting fraction is 6/11. Find the original fraction<BR>\n" );
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document.write( "Let the original fraction be x/y.<BR>\n" );
document.write( "Equations:<BR>\n" );
document.write( "(x+5)/(y-1) = 8/3<BR>\n" );
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document.write( "(2x)/(y+7)/ 6/11<BR>\n" );
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document.write( "Rearrange:<BR>\n" );
document.write( "3(x+5) = 8(y-1)<BR>\n" );
document.write( "11(2x) = 6(y+7)<BR>\n" );
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document.write( "Modify:<BR>\n" );
document.write( "8y - 3x = 23<BR>\n" );
document.write( "6y -22x = -42<BR>\n" );
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document.write( "Set up for elimination:<BR>\n" );
document.write( "48y - 18x = 6*23<BR>\n" );
document.write( "48y -176x = 8*-42<BR>\n" );
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document.write( "Subtract the 2nd equation from the 1st to solve for \"x\":<BR>\n" );
document.write( "158x = 474<BR>\n" );
document.write( "x = 3<BR>\n" );
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document.write( "Substitute into 8y -3x = 23 to solve for \"y\":<BR>\n" );
document.write( "8y -3*3 = 23<BR>\n" );
document.write( "8y - 9 = 23<BR>\n" );
document.write( "8y = 32<BR>\n" );
document.write( "y = 4<BR>\n" );
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document.write( "Original fraction: x/y = 3/4<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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