document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=176375>Question 176375</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The members of a flying club plan to share equally the cost of a $200,000 airplane.  The members want to find five more people to join the club so that the cost per person will decrease by $2,000.  How many members are currently in the club? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #131467 by </B><A HREF=/tutors/aboutme.mpl?userid=EMStelley><B>EMStelley(208)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=EMStelley><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=EMStelley><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=131467\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Call the number of people currently in the club x.  Then if they share the cost equally, they will each pay $200,000/x.  Now, if they find 5 more people the cost will decrease by 2,000 per person.  So if x is increased by 5, (x+5), the cost, $200,000/(x+5) will be 2,000 less per person, a.k.a. $200,000/x - 2000.  So we need to set those two equal to each other and solve for x.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=200000%2F%28x%2B5%29=200000%2Fx-2000 ALIGN=MIDDLE  ALT=\"200000%2F%28x%2B5%29=200000%2Fx-2000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now, if you are anything like most people, than I would assume you don't like working with fractions.  So how about we try to get rid of them?  If we multiplied both sides by x would that work?  No, it would not get rid of the fraction on the left hand side.  If we multiplied both sides by x+5 would that work?  No again, as it would not correct the fraction on the right hand side.  It seems that we need both.  So let's multiply by x(x+5) on both sides:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=200000x=200000%28x%2B5%29-2000x%28x%2B5%29 ALIGN=MIDDLE  ALT=\"200000x=200000%28x%2B5%29-2000x%28x%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=200000x=200000x%2B1000000-2000x%5E2-10000x ALIGN=MIDDLE  ALT=\"200000x=200000x%2B1000000-2000x%5E2-10000x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now, subtract 200000x from both sides to obtain:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=1000000-2000x%5E2-10000x ALIGN=MIDDLE  ALT=\"0=1000000-2000x%5E2-10000x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Rearranging, we have a quadratic:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2000x%5E2-10000x%2B1000000=0 ALIGN=MIDDLE  ALT=\"-2000x%5E2-10000x%2B1000000=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now, these are all fairly large numbers.  Do they have anything in common?  They all have at least a factor of 2000 in them, so let's divide both sides by -2000 to get rid of it:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B5x-500=0 ALIGN=MIDDLE  ALT=\"x%5E2%2B5x-500=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So now, we need to solve this quadratic equation.  I will use the quadratic formula:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "Here, a=1, b=5, c=-500, so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-5+%2B-+sqrt%28+5%5E2-4%2A1%2A-500+%29%29%2F%282%2A1%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-5+%2B-+sqrt%28+5%5E2-4%2A1%2A-500+%29%29%2F%282%2A1%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+=+%28-5+%2B-+sqrt%2825%2B2000%29%29%2F2 ALIGN=MIDDLE  ALT=\"x+=+%28-5+%2B-+sqrt%2825%2B2000%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-5+%2B-+sqrt%282025%29%29%2F2 ALIGN=MIDDLE  ALT=\"x+=+%28-5+%2B-+sqrt%282025%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-5+%2B-+45%29%2F2 ALIGN=MIDDLE  ALT=\"x+=+%28-5+%2B-+45%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=40%2F2=20 ALIGN=MIDDLE  ALT=\"x=40%2F2=20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-50%2F2=-25 ALIGN=MIDDLE  ALT=\"x=-50%2F2=-25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "However, it's not possible to have -25 people in a club, so the only feasible solution here is 20.<BR>\n" );
document.write( " </SPAN>\n" );
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