document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=132927>Question 132927</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If the numerator and denominator of a fraction are both decreased by three, the fraction becomes 4\5. If the numerator and denominator are both increased by three, the fraction becomes 7\8.\r<BR>\n" );
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document.write( "1.  Write down two equations from the statement?<BR>\n" );
document.write( "2.  Solve the equations simultaneously to get 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 #97133 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=97133\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "Let x=numerator of original fraction<BR>\n" );
document.write( "And let y=denominator of original fraction\r<BR>\n" );
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document.write( "We are told that:<BR>\n" );
document.write( "(x-3)/(y-3)=4/5   multiply each side by 5(y-3)<BR>\n" );
document.write( "5(x-3)=4(y-3)  get rid of parens<BR>\n" );
document.write( "5x-15=4y-12 subtract 4y from and add 15 to both sides<BR>\n" );
document.write( "5x-15+15-4y=4y-4y-12+15 collect like terms<BR>\n" );
document.write( "5x-4y=3---------------------------------------------eq1\r<BR>\n" );
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document.write( "We are also told that:<BR>\n" );
document.write( "(x+3)/(y+3)=7/8  multiply each side by 8(y+3)<BR>\n" );
document.write( "8(x+3)=7(y+3)  get rid of parens<BR>\n" );
document.write( "8x+24=7y+21  subtract 7y and also 24 from both sides<BR>\n" );
document.write( "8x-7y+24-24=7y-7y+21-24  collect like terms\r<BR>\n" );
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document.write( "8x-7y=-3------------------------------------------eq2<BR>\n" );
document.write( "Multiply each term in eq1 by 8<BR>\n" );
document.write( "40x-32y=24-----------------------------------eq1a<BR>\n" );
document.write( "Multiply each term in eq2 by 5<BR>\n" );
document.write( "40x-35y=-15-------------------------------------eq2a\r<BR>\n" );
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document.write( "subtract eq1a from eq2a\r<BR>\n" );
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document.write( "-3y=-39  divide both sides by -3<BR>\n" );
document.write( "y=13--------------------------------------denominator of original fraction\r<BR>\n" );
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document.write( "Substitute y=13 into eq1<BR>\n" );
document.write( "5x-4*13=3<BR>\n" );
document.write( "5x-52=3 add 52 to both sides<BR>\n" );
document.write( "5x-52+52=3+52  collect like terms<BR>\n" );
document.write( "5x=55  divide both sides by 5<BR>\n" );
document.write( "x=11-------------------------------------numerator of original fraction\r<BR>\n" );
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document.write( "CK<BR>\n" );
document.write( "(11-3)/(13-3)=4/5<BR>\n" );
document.write( "8/10=4/5<BR>\n" );
document.write( "4/5=4/5<BR>\n" );
document.write( "also<BR>\n" );
document.write( "(11+3)/(13+3)=7/8<BR>\n" );
document.write( "14/16=7/8<BR>\n" );
document.write( "7/8=7/8\r<BR>\n" );
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document.write( "Hope this helps----ptaylor </SPAN>\n" );
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