document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=22160>Question 22160</A>: <I><SPAN STYLE=\"word-break: break-all;\">   Hello.  I have been workingon this problem all night and I know it's probably something I'm overlooking.  Please help.\r<BR>\n" );
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document.write( "2. Some students planned for a get-together. The budget for food was $500. Five of the students failed to come because of the distance and therefore the cost of food for each member increased by $5. How many students attended the get-together? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #10690 by </B><A HREF=/tutors/aboutme.mpl?userid=longjonsilver><B>longjonsilver(2297)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=longjonsilver><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=longjonsilver><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=10690\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let number of student originally = x<BR>\n" );
document.write( "Therefore number of students who actually turn up = x-5\r<BR>\n" );
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document.write( "Original cost per head = 500/x whereas the actual Cost per head = 500/(x-5)\r<BR>\n" );
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document.write( "Now, the actual cost (per head) - original cost (per head) = 5. So,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=500%2F%28x-5%29+-+500%2Fx+=+5 ALIGN=MIDDLE  ALT=\"500%2F%28x-5%29+-+500%2Fx+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Now get rid of the fractions by multiplying every term by x(x-5). Some cancelling happens and we are left with:\r<BR>\n" );
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document.write( "500x - 500(x-5) = 5x(x-5).\r<BR>\n" );
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document.write( "We need to multiply this out, collect terms and then solve the resulting quadratic:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=500x+-+500x+%2B+2500+=+5x%5E2+-+25x%29 ALIGN=MIDDLE  ALT=\"500x+-+500x+%2B+2500+=+5x%5E2+-+25x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2500+=+5x%5E2+-+25x%29 ALIGN=MIDDLE  ALT=\"2500+=+5x%5E2+-+25x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%5E2+-+25x+-+2500+=+0%29 ALIGN=MIDDLE  ALT=\"5x%5E2+-+25x+-+2500+=+0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+5x+-+500+=+0%29 ALIGN=MIDDLE  ALT=\"x%5E2+-+5x+-+500+=+0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(x + 20)(x - 25) = 0\r<BR>\n" );
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document.write( "so either x+20 = 0 OR x-25 = 0<BR>\n" );
document.write( "so either x = -20 or x = 25\r<BR>\n" );
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document.write( "As x is the number of students, we cannot have a negative, so the answer we require is 25.\r<BR>\n" );
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document.write( "CHECK:<BR>\n" );
document.write( "500/25 --> $20 per head\r<BR>\n" );
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document.write( "then down to 20 students, 500/20 --> $25 per head.\r<BR>\n" );
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document.write( "So this is correct, the price did increase by $5 per head.\r<BR>\n" );
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document.write( "jon.<BR>\n" );
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