document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=170726>Question 170726</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0618503080/algebrahomeworkh>intermediate algebra</A><BR>\n" );
document.write( ": <I><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? \r<BR>\n" );
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document.write( "Not sure how to do these word problems and will appreciate any help, so far I have a B in class :) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #126034 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=126034\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let c=cost per individual (the cost before the students failed to arrive) and n=number of students\r<BR>\n" );
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document.write( "So the total cost is divided among n people to get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=500%2Fn ALIGN=MIDDLE  ALT=\"c=500%2Fn\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since 5 failed to attend, this means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n-5 ALIGN=MIDDLE  ALT=\"n-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > students showed up. Now the new cost is\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%2B5=500%2F%28n-5%29 ALIGN=MIDDLE  ALT=\"c%2B5=500%2F%28n-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%2B5=500%2F%28n-5%29 ALIGN=MIDDLE  ALT=\"c%2B5=500%2F%28n-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=500%2Fn%2B5=500%2F%28n-5%29 ALIGN=MIDDLE  ALT=\"500%2Fn%2B5=500%2F%28n-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=500%2Fn ALIGN=MIDDLE  ALT=\"c=500%2Fn\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=500%28n-5%29%2B5n%28n-5%29=500n ALIGN=MIDDLE  ALT=\"500%28n-5%29%2B5n%28n-5%29=500n\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply every term by the LCD <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%28n-5%29 ALIGN=MIDDLE  ALT=\"n%28n-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This cancels out every denominator.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=500n-2500%2B5n%5E2-25n=500n ALIGN=MIDDLE  ALT=\"500n-2500%2B5n%5E2-25n=500n\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=500n-2500%2B5n%5E2-25n-500n=0 ALIGN=MIDDLE  ALT=\"500n-2500%2B5n%5E2-25n-500n=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=500n ALIGN=MIDDLE  ALT=\"500n\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5n%5E2-25n-2500=0 ALIGN=MIDDLE  ALT=\"5n%5E2-25n-2500=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=500n ALIGN=MIDDLE  ALT=\"500n\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides.\r<BR>\n" );
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document.write( "Let's use the quadratic formula to solve for n\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 ALIGN=MIDDLE  ALT=\"n+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the quadratic formula\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n+=+%28-%28-25%29+%2B-+sqrt%28+%28-25%29%5E2-4%285%29%28-2500%29+%29%29%2F%282%285%29%29 ALIGN=MIDDLE  ALT=\"n+=+%28-%28-25%29+%2B-+sqrt%28+%28-25%29%5E2-4%285%29%28-2500%29+%29%29%2F%282%285%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=5 ALIGN=MIDDLE  ALT=\"a=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-25 ALIGN=MIDDLE  ALT=\"b=-25\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=-2500 ALIGN=MIDDLE  ALT=\"c=-2500\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n+=+%2825+%2B-+sqrt%28+%28-25%29%5E2-4%285%29%28-2500%29+%29%29%2F%282%285%29%29 ALIGN=MIDDLE  ALT=\"n+=+%2825+%2B-+sqrt%28+%28-25%29%5E2-4%285%29%28-2500%29+%29%29%2F%282%285%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Negate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-25 ALIGN=MIDDLE  ALT=\"-25\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25 ALIGN=MIDDLE  ALT=\"25\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n+=+%2825+%2B-+sqrt%28+625-4%285%29%28-2500%29+%29%29%2F%282%285%29%29 ALIGN=MIDDLE  ALT=\"n+=+%2825+%2B-+sqrt%28+625-4%285%29%28-2500%29+%29%29%2F%282%285%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-25 ALIGN=MIDDLE  ALT=\"-25\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=625 ALIGN=MIDDLE  ALT=\"625\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n+=+%2825+%2B-+sqrt%28+625--50000+%29%29%2F%282%285%29%29 ALIGN=MIDDLE  ALT=\"n+=+%2825+%2B-+sqrt%28+625--50000+%29%29%2F%282%285%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%285%29%28-2500%29 ALIGN=MIDDLE  ALT=\"4%285%29%28-2500%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-50000 ALIGN=MIDDLE  ALT=\"-50000\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n+=+%2825+%2B-+sqrt%28+625%2B50000+%29%29%2F%282%285%29%29 ALIGN=MIDDLE  ALT=\"n+=+%2825+%2B-+sqrt%28+625%2B50000+%29%29%2F%282%285%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28625--50000%29 ALIGN=MIDDLE  ALT=\"sqrt%28625--50000%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28625%2B50000%29 ALIGN=MIDDLE  ALT=\"sqrt%28625%2B50000%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n+=+%2825+%2B-+sqrt%28+50625+%29%29%2F%282%285%29%29 ALIGN=MIDDLE  ALT=\"n+=+%2825+%2B-+sqrt%28+50625+%29%29%2F%282%285%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=625 ALIGN=MIDDLE  ALT=\"625\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=50000 ALIGN=MIDDLE  ALT=\"50000\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=50625 ALIGN=MIDDLE  ALT=\"50625\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n+=+%2825+%2B-+sqrt%28+50625+%29%29%2F%2810%29 ALIGN=MIDDLE  ALT=\"n+=+%2825+%2B-+sqrt%28+50625+%29%29%2F%2810%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10 ALIGN=MIDDLE  ALT=\"10\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n+=+%2825+%2B-+225%29%2F%2810%29 ALIGN=MIDDLE  ALT=\"n+=+%2825+%2B-+225%29%2F%2810%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=50625 ALIGN=MIDDLE  ALT=\"50625\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=225 ALIGN=MIDDLE  ALT=\"225\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n+=+%2825+%2B+225%29%2F%2810%29 ALIGN=MIDDLE  ALT=\"n+=+%2825+%2B+225%29%2F%2810%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n+=+%2825+-+225%29%2F%2810%29 ALIGN=MIDDLE  ALT=\"n+=+%2825+-+225%29%2F%2810%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the expression. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n+=+%28250%29%2F%2810%29 ALIGN=MIDDLE  ALT=\"n+=+%28250%29%2F%2810%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n+=++%28-200%29%2F%2810%29 ALIGN=MIDDLE  ALT=\"n+=++%28-200%29%2F%2810%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n+=+25 ALIGN=MIDDLE  ALT=\"n+=+25\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n+=+-20 ALIGN=MIDDLE  ALT=\"n+=+-20\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify. \r<BR>\n" );
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document.write( "Since a negative amount of people doesn't make any sense, this means that the only answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n+=+25 ALIGN=MIDDLE  ALT=\"n+=+25\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So 25 people were going to attend but only 20 actually attended.\r<BR>\n" );
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