document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=663702>Question 663702</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A group of small business owners pledge a total of 1,000 a month to beautify the mall. The owners agreed to split the cause equally. When 5 went out of business, the rest had to pay an addition 10 per month each. How many were in the original group? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #412903 by </B><A HREF=/tutors/aboutme.mpl?userid=SwiftAlbatross><B>SwiftAlbatross(13)</B></A><img src=\"/images/stars/stars-06.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=SwiftAlbatross><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=SwiftAlbatross><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=412903\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x = the number of original business owners\r<BR>\n" );
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document.write( "$1000 / x = the amount each business owner paid\r<BR>\n" );
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document.write( "When 5 business owners were lost, there were x - 5 left and they had to pay what the 5 business owners would not. The 5 business owners paid\r<BR>\n" );
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document.write( "5 * ($1000 / x)\r<BR>\n" );
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document.write( "so we now pay this with $10 each from the remaining business owners\r<BR>\n" );
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document.write( "5 * ($1000 / x) = $10 * (x - 5)\r<BR>\n" );
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document.write( "Doing some algebra, we get\r<BR>\n" );
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document.write( "5 * 1000 / x = 10 (x - 5)\r<BR>\n" );
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document.write( "5000 = 10 * x * (x - 5)<BR>\n" );
document.write( "500 = x^2 - 5x<BR>\n" );
document.write( "x^2 - 5x - 500 = 0<BR>\n" );
document.write( "(x - 25) * (x + 20) = 0<BR>\n" );
document.write( "x = 25 OR x = -20\r<BR>\n" );
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document.write( "x can only be positive so x must be 25.\r<BR>\n" );
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document.write( "Checking the answer, we get 25 original business owners paying $1000 / 25, or $40 each. When 5 fold, there are 20 left and they have to pay the difference. Five business owners would have paid 5 * $40 which equals $200. The 20 remaining business owners pay $10 each so $10 * 20 equals to $200, so this is correct.\r<BR>\n" );
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document.write( "Therefore, there were 25 business owners in the original group. </SPAN>\n" );
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