document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1061283>Question 1061283</A>: <I><SPAN STYLE=\"word-break: break-all;\"> When a number is decreased by its reciprocal, the result is 2 1/10 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #676149 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=676149\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let x be the number.\r<BR>\n" );
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document.write( "you get x - 1/x = 21/10\r<BR>\n" );
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document.write( "multiply both sides of this equation by 10x to get:\r<BR>\n" );
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document.write( "10x^2 - 10 = 21x\r<BR>\n" );
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document.write( "subtract 21x from both sides of the equation to get:\r<BR>\n" );
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document.write( "10x^2 - 21x - 10 = 0\r<BR>\n" );
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document.write( "solve this quadratic equation to get:\r<BR>\n" );
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document.write( "x = -.4 or x = 2.5\r<BR>\n" );
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document.write( "replace x in the original equation with each of these values and you will see that both values are valid.\r<BR>\n" );
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document.write( "your solution is that the number will either be 2.5 or -.4.\r<BR>\n" );
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document.write( "however, when x = -.4 and you subtract it's reciprocal, you get 2.1 which is larger than -.4, so, even though you subtracted it's reciprocal from it, you wound up with a larger number, which may not be considered a decrease.\r<BR>\n" );
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document.write( "that leaves you with 2.5 as your number.\r<BR>\n" );
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document.write( "the answer could be either but, if you need just one number, i would go with 2.5.\r<BR>\n" );
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document.write( "it all comes down to determining what they mean by decrease.\r<BR>\n" );
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document.write( "technically, when you decrease a number by something, you are subtracting that something from it, but this gets topsy turvy when you are dealing with negative numbers, because when you subtract a negative number, you are effectively adding a positive number, which is an increase.\r<BR>\n" );
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document.write( "if i had to guess what they're looking for, i would guess that they're looking for 2.5 as the answer.\r<BR>\n" );
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document.write( "but i could be wrong, depending on what they're really looking for.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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