document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=170960>Question 170960</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 94. Sharing cost. The members of a flying club plan to share<BR>\n" );
document.write( "equally the cost of a $200,000 airplane. The members<BR>\n" );
document.write( "want to find five more people to join the club so that the<BR>\n" );
document.write( "cost per person will decrease by $2000. How many members<BR>\n" );
document.write( "are currently in the club?<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 #126235 by </B><A HREF=/tutors/aboutme.mpl?userid=Mathtut><B>Mathtut(3670)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Mathtut><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=126235\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 200000/x=c   where x is the number of people in the club<BR>\n" );
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document.write( "200000/x+5=c-2000<BR>\n" );
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document.write( "so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=200000%2F%28x%2B5%29=%28200000%2Fx%29-2000 ALIGN=MIDDLE  ALT=\"200000%2F%28x%2B5%29=%28200000%2Fx%29-2000\"   DISABLED_style= \"max-width:90%; height:auto;\" >---> multiply all terms by x(x+5)<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=200000x=200000%28x%2B5%29-2000%28x%5E2%2B5x%29 ALIGN=MIDDLE  ALT=\"200000x=200000%28x%2B5%29-2000%28x%5E2%2B5x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >distribute<BR>\n" );
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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;\" > 200000x terms cancel each other and divide rest of terms by 2000.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x%5E2-5x%2B500=0 ALIGN=MIDDLE  ALT=\"-x%5E2-5x%2B500=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >--->x^2+5x-500=0}}}\r<BR>\n" );
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document.write( "20 and -25 are the values for x but we know there arent negative people so 20 is our value for x meaning that<BR>\n" );
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document.write( "THERE ARE CURRENTLY<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20 ALIGN=MIDDLE  ALT=\"20\"   DISABLED_style= \"max-width:90%; height:auto;\" > PEOPLE IN THE CLUB\r<BR>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=quadratic.solver>SOLVE quadratic equation with variable</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Quadratic equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1x%5E2%2B5x%2B-500+=+0 ALIGN=MIDDLE  ALT=\"1x%5E2%2B5x%2B-500+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) has the following solutons:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  For these solutions to exist, the <U>discriminant</U> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" > should not be a negative number.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  First, we need to compute the discriminant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" >: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac=%285%29%5E2-4%2A1%2A-500=2025 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%285%29%5E2-4%2A1%2A-500=2025\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=2025 is greater than zero. That means that there are two solutions: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5B12%5D+=+%28-5%2B-sqrt%28+2025+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-5%2B-sqrt%28+2025+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+=+%28-%285%29%2Bsqrt%28+2025+%29%29%2F2%5C1+=+20 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%285%29%2Bsqrt%28+2025+%29%29%2F2%5C1+=+20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+=+%28-%285%29-sqrt%28+2025+%29%29%2F2%5C1+=+-25 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%285%29-sqrt%28+2025+%29%29%2F2%5C1+=+-25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <BR>\n" );
document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1x%5E2%2B5x%2B-500 ALIGN=MIDDLE  ALT=\"1x%5E2%2B5x%2B-500\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be factored:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1x%5E2%2B5x%2B-500+=+1%28x-20%29%2A%28x--25%29 ALIGN=MIDDLE  ALT=\"1x%5E2%2B5x%2B-500+=+1%28x-20%29%2A%28x--25%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 20, -25.\n" );
document.write( "Here's your graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B5%2Ax%2B-500+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B5%2Ax%2B-500+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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