document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=106572>Question 106572</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0321233832/algebrahomeworkh></A><BR>\n" );
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document.write( "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?\r<BR>\n" );
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document.write( "500/x + 5 = 500/(x-5)<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #77574 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=77574\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 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?<BR>\n" );
document.write( "500/x + 5 = 500/(x-5)<BR>\n" );
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document.write( "I would do it this way:<BR>\n" );
document.write( "Let x = actual number that attended:<BR>\n" );
document.write( "Then<BR>\n" );
document.write( "(x+5) = number that was anticipated to come<BR>\n" );
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document.write( "Anticipated cost + $5 = Actual cost<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=500%2F%28%28x%2B5%29%29 ALIGN=MIDDLE  ALT=\"500%2F%28%28x%2B5%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + 5 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=500%2Fx ALIGN=MIDDLE  ALT=\"500%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Multiply equation by x(x+5)<BR>\n" );
document.write( "500x + 5(x(x+5)) = 500(x+5)<BR>\n" );
document.write( "500x + 5x^2 + 25x = 500x + 2500<BR>\n" );
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document.write( "Arrange as a quadratic on the left:<BR>\n" );
document.write( "5x^2 + 500x - 500x + 25x - 2500 = 0<BR>\n" );
document.write( "5x^2 + 25x - 2500 = 0<BR>\n" );
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document.write( "Simplify, divide by 5<BR>\n" );
document.write( "x^2 + 5x - 500 = 0<BR>\n" );
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document.write( "Factors to:<BR>\n" );
document.write( "(x+25)(x-20) = 0<BR>\n" );
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document.write( "x = +20 is the solution we want here<BR>\n" );
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document.write( "20 actually attended<BR>\n" );
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document.write( "Actual cost 500/20 = $25 each<BR>\n" );
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document.write( "If 25 attended:<BR>\n" );
document.write( "500/25 = $20, $5 less </SPAN>\n" );
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