document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1120967>Question 1120967</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A student plans to spend ¢200 on p notebooks. But the price of the notebooks had increased by ¢10. As a result, the number of notebooks the student could buy was reduced by 1. Find the price of each notebook before the increase.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #736697 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=736697\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> student plans to spend 200 on p notebooks.<BR>\n" );
document.write( "if the price goes up by 10, the student can buy p - 1 notebooks.\r<BR>\n" );
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document.write( "let x = the price of one notebook.\r<BR>\n" );
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document.write( "you have two equations that need to be solved simultaneously.\r<BR>\n" );
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document.write( "they are:\r<BR>\n" );
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document.write( "x * p = 200<BR>\n" );
document.write( "(x+10) * (p-1) = 200\r<BR>\n" );
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document.write( "solve for x in the first equation to get x = 200/p\r<BR>\n" );
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document.write( "replace x in the second equation by 200/p to get:\r<BR>\n" );
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document.write( "(x+10) * (p-1) = 200 becomes:\r<BR>\n" );
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document.write( "(200/p + 10) * (p-1) = 200\r<BR>\n" );
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document.write( "multiply both sides of this equation by p to get:\r<BR>\n" );
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document.write( "p * (200/p + 10) * (p-1) = 200 * p\r<BR>\n" );
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document.write( "since p * (200/p + 10) is equal to 200 + 10p, the equation becomes:\r<BR>\n" );
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document.write( "(200 + 10p) * (p-1) = 200p\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "200p - 200 + 10p * p - 10p = 200p\r<BR>\n" );
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document.write( "the 200p in both sides of the equation cancels out and you are left with:\r<BR>\n" );
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document.write( "-200 + 10p^2 - 10p = 0\r<BR>\n" );
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document.write( "rearrange the terms in descending order of degree to get:\r<BR>\n" );
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document.write( "10p^2 - 10p - 200 = 0\r<BR>\n" );
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document.write( "divide both sides of the equation by 10 to get:\r<BR>\n" );
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document.write( "p^2 - p - 20 = 0\r<BR>\n" );
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document.write( "factor this quadratic equation to get:\r<BR>\n" );
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document.write( "(p-5)*(p+4) = 0\r<BR>\n" );
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document.write( "solve for p to get p = 5 or p = -4\r<BR>\n" );
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document.write( "your solution is p = 5.\r<BR>\n" );
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document.write( "when p = 5, x * p = 200 becomes x * 5 = 200 which makes x = 40\r<BR>\n" );
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document.write( "when p = 4, x * p = 200 becomes x * 4 = 200 which makes x = 50\r<BR>\n" );
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document.write( "x is the price of each notebook.\r<BR>\n" );
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document.write( "when the price is 40, you can buy 200 / 40 = 5 notebooks.\r<BR>\n" );
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document.write( "when the price is raised by 10 to be equal to 50, you can buy 200 / 50 = 4 notebooks which is 1 less than when the price was 40.\r<BR>\n" );
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document.write( "your solution is that the price of each notebook was 40 before the increase.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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