document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=511476>Question 511476</A>: <I><SPAN STYLE=\"word-break: break-all;\"> can someone help me with this one..\r<BR>\n" );
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document.write( "If the numerator and the denominator of a certain fraction are each decreased by 2, the value of the new fraction is 1/2. but if the numerator of the original fraction is increased by 1 and the denominator decreased by 2, the resulting fraction is equal to 3/4. Find the original fraction.\r<BR>\n" );
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document.write( "thank you! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #342230 by </B><A HREF=/tutors/aboutme.mpl?userid=oberobic><B>oberobic(2304)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=oberobic><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=342230\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The original fraction is x/y.<BR>\n" );
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document.write( "We're told:<BR>\n" );
document.write( "x-2 / y -2 = 1/2<BR>\n" );
document.write( "so<BR>\n" );
document.write( "2(x-2) = y-2<BR>\n" );
document.write( "2x -4 = y -2<BR>\n" );
document.write( "2x -2 = y<BR>\n" );
document.write( "so<BR>\n" );
document.write( "y = 2x -2<BR>\n" );
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document.write( "We're also told:<BR>\n" );
document.write( "x+1 / y-2 = 3/4<BR>\n" );
document.write( "so<BR>\n" );
document.write( "4x+4 = 3y-6<BR>\n" );
document.write( "3y = 4x + 10<BR>\n" );
document.write( "y = 4/3x + 10/3<BR>\n" );
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document.write( "Now we have two linear equations and two unknowns.<BR>\n" );
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document.write( "We can graph them see where the intersect.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28500%2C500%2C-5%2C15%2C-5%2C15%2C2%2Ax-2%2C4%2F3%2Ax%2B10%2F3%29 ALIGN=MIDDLE  ALT=\"graph%28500%2C500%2C-5%2C15%2C-5%2C15%2C2%2Ax-2%2C4%2F3%2Ax%2B10%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Or we can solve the two equations.<BR>\n" );
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document.write( "y = 2x -2<BR>\n" );
document.write( "3y = 4x + 10<BR>\n" );
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document.write( "3y = 6x -6<BR>\n" );
document.write( "3y = 4x +10<BR>\n" );
document.write( "0 = 2x -16<BR>\n" );
document.write( "2x = 16<BR>\n" );
document.write( "x = 8<BR>\n" );
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document.write( "substitute<BR>\n" );
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document.write( "y = 2(8) -2<BR>\n" );
document.write( "y = 14<BR>\n" );
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document.write( "So it appears the first equation is<BR>\n" );
document.write( "8/14<BR>\n" );
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document.write( "But always check your answer<BR>\n" );
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document.write( "(x-2)/(y-2) = 6/12 = 1/2<BR>\n" );
document.write( "(x+1)/(y-2) = 9/12 = 3/4<BR>\n" );
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document.write( "Answer:  x=8, y=14<BR>\n" );
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document.write( "Done. </SPAN>\n" );
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