document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=363090>Question 363090</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If we increased  x and y by 10%, by what percent does (x) /(x + y) change ? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #258834 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=258834\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> increase by 10% means you multiply by 1.10.\r<BR>\n" );
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document.write( "x + .10 * x = (1 + .10)*x = 1.10 * x<BR>\n" );
document.write( "y + .10 * y = (1 + .10)*y = 1.10 * y\r<BR>\n" );
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document.write( "1.10 * (x + y) = 1.10 * x + 1.10 * y\r<BR>\n" );
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document.write( "your first ratio is x / (x + y)\r<BR>\n" );
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document.write( "your second ratio is 1.10x / 1/10 * (x + y)\r<BR>\n" );
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document.write( "you have a common factor of 1.10 which cancels out and you are left with x / (x + y)\r<BR>\n" );
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document.write( "since that's what you started with, the ratio becomes the same, i.e. there is a 0% change.\r<BR>\n" );
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document.write( "here's how it works.\r<BR>\n" );
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document.write( "assume x = 100 and y = 400\r<BR>\n" );
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document.write( "x / (x + y) = 100 / 500 = 1/5 = .2\r<BR>\n" );
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document.write( "increase both x and y by 10% to get:\r<BR>\n" );
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document.write( "x = 110 and y = 440\r<BR>\n" );
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document.write( "x + y = 110 + 440 = 550\r<BR>\n" );
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document.write( "take 110 / 550 = 1/5 = .2\r<BR>\n" );
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document.write( "the ratio is the same therefore the change in the ratio is 0.\r<BR>\n" );
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document.write( "if you look at 110 / 550, you will see that 110 = 100 * 1.1 and 550 = 500 * 1.10\r<BR>\n" );
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document.write( "if you take 1.10 * 100 / 1.10 * 500 you can see that the 1.10 in the numerator and in the denominator cancel out to get 100 / 500 which is what you started with.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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