document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=896212>Question 896212</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A club can elect a member as president and another member as treasurer in 506 different ways. How many members does the club have?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #543327 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=543327\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's say we had x members total\r<BR>\n" );
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document.write( "That means we have x choices for president (assuming they are all candidates). \r<BR>\n" );
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document.write( "That leaves us with x-1 choices for treasurer. We cannot pick the same person to run both positions.\r<BR>\n" );
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document.write( "So we have x*(x-1) ways to pick 2 people (from a pool of x people)\r<BR>\n" );
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document.write( "We know that there are 506 ways to do this, so x*(x-1) = 506\r<BR>\n" );
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document.write( "Solve for x\r<BR>\n" );
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document.write( "x*(x-1) = 506\r<BR>\n" );
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document.write( "x^2-x = 506\r<BR>\n" );
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document.write( "x^2-x-506 = 0\r<BR>\n" );
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document.write( "Use the quadratic formula to get the solutions x = 23 or x = -22. \r<BR>\n" );
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document.write( "I show the steps in solving <a  rel=nofollow HREF=\"http://www.algebra.com/algebra/homework/quadratic/Quadratic_Equations.faq.question.896220.html\">here</a>.\r<BR>\n" );
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document.write( "x is the number of people, so it has to be a positive whole number. That means we ignore x = -22\r<BR>\n" );
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document.write( "The only practical solution is x = 23.\r<BR>\n" );
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document.write( "That means the club has <font size=4 color=\"red\">23 members</font>.\r<BR>\n" );
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document.write( "Notice how\r<BR>\n" );
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document.write( "x*(x-1) = 506\r<BR>\n" );
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document.write( "23*(23-1) = 506\r<BR>\n" );
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document.write( "23*22 = 506\r<BR>\n" );
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document.write( "506 = 506\r<BR>\n" );
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document.write( "So that confirms the answer.\r<BR>\n" );
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