document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=896704>Question 896704</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A speculator sold some shares of stock for $2880. Several days later, the stock having dropped in price $2 per share, he repurchased, for the same amount of money, 6 more shares than he sold. How many shares did he sell? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #543720 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=543720\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x = number of shares he sold.<BR>\n" );
document.write( "p = price per share he sold at.\r<BR>\n" );
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document.write( "you get x*p = 2880\r<BR>\n" );
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document.write( "price went down 2 and he bought back 6 more shares at the same total price.\r<BR>\n" );
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document.write( "you get (x+6) * (p-2) = 2880\r<BR>\n" );
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document.write( "since they both equal 2880, you can set x*p equal to (x+6)*(p-2).\r<BR>\n" );
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document.write( "your equation to solve is:\r<BR>\n" );
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document.write( "x*p = (x+6) * (p-2)\r<BR>\n" );
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document.write( "simplify this equation to get:\r<BR>\n" );
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document.write( "x*p = x*p - 2x + 6p - 12\r<BR>\n" );
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document.write( "subtract x*p from both sides of this equation to get:\r<BR>\n" );
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document.write( "0 = -2x + 6p - 12\r<BR>\n" );
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document.write( "from x*p = 2880, you can solve for p to get:\r<BR>\n" );
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document.write( "p = 2880 / x\r<BR>\n" );
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document.write( "replace p in the equation of 0 = -2x + 6p - 12 to get:\r<BR>\n" );
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document.write( "0 = -2x + 6(2880/x) - 12\r<BR>\n" );
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document.write( "multiply both sides of this equation by x to get:\r<BR>\n" );
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document.write( "0 = -2x^2 + 6*2880 - 12\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "0 = -2x^2 + 17280 - 12x\r<BR>\n" );
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document.write( "divide both sides of this equation by -2 to get:\r<BR>\n" );
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document.write( "0 = x^2 - 8640 + 6x\r<BR>\n" );
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document.write( "rearrange the terms in descending order of degrees of x to get:\r<BR>\n" );
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document.write( "0 = x^2 + 6x - 8640\r<BR>\n" );
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document.write( "factor x^2 + 6x - 8640 to get:\r<BR>\n" );
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document.write( "0 = (x+96) * (x-90)\r<BR>\n" );
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document.write( "solve for x to get:\r<BR>\n" );
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document.write( "x = -96 or x = 90\r<BR>\n" );
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document.write( "since x has to be positive, your solution appears to be x = 90\r<BR>\n" );
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document.write( "when x = 90, p = 2880 / 90 = 32\r<BR>\n" );
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document.write( "he sold 90 shares at 32 dollars apiece to get 2880.\r<BR>\n" );
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document.write( "later he bought back 96 shares at 30 dollars apiece for a total cost of 2880.\r<BR>\n" );
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document.write( "numbers check out so your solution is:\r<BR>\n" );
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document.write( "he sold 90 shares.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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