document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=201205>Question 201205</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help finding the formula to solve this word problem. 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 $2000. 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 #151412 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=151412\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x=# of people in the club (before 5 more join)\r<BR>\n" );
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document.write( "Before they get 5 people, we have the equation:\r<BR>\n" );
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document.write( "Cost Per Individual:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=200000%2Fx ALIGN=MIDDLE  ALT=\"c=200000%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" >  (since the cost is divided among \"x\" people)\r<BR>\n" );
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document.write( "When 5 more people join, the equation becomes\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c-2000=200000%2F%28x%2B5%29 ALIGN=MIDDLE  ALT=\"c-2000=200000%2F%28x%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (simply replace \"x\" with \"x+5\" and subtract 2000 from \"c\" to form the new equation)\r<BR>\n" );
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document.write( "So we have the two equations\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=200000%2Fx ALIGN=MIDDLE  ALT=\"c=200000%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > Equation 1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c-2000=200000%2F%28x%2B5%29 ALIGN=MIDDLE  ALT=\"c-2000=200000%2F%28x%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Equation 2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c-2000=200000%2F%28x%2B5%29 ALIGN=MIDDLE  ALT=\"c-2000=200000%2F%28x%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with Equation 2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=200000%2Fx-2000=200000%2F%28x%2B5%29 ALIGN=MIDDLE  ALT=\"200000%2Fx-2000=200000%2F%28x%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=150000%2Fx ALIGN=MIDDLE  ALT=\"c=150000%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > (which is Equation 1)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cross%28x%29%28x%2B5%29%28200000%2Fcross%28x%29%29-x%28x%2B5%29%282000%29=x%2Across%28%28x%2B5%29%29%28200000%2Fcross%28%28x%2B5%29%29%29 ALIGN=MIDDLE   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=x%28x%2B5%29 ALIGN=MIDDLE  ALT=\"x%28x%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to clear out the fractions.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=200000%28x%2B5%29-2000x%28x%2B5%29=200000x ALIGN=MIDDLE  ALT=\"200000%28x%2B5%29-2000x%28x%2B5%29=200000x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply and simplify.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=200000x%2B1000000-2000x%5E2-10000x=200000x ALIGN=MIDDLE  ALT=\"200000x%2B1000000-2000x%5E2-10000x=200000x\"   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=200000x%2B1000000-2000x%5E2-10000x-200000x=0 ALIGN=MIDDLE  ALT=\"200000x%2B1000000-2000x%5E2-10000x-200000x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 200000x from both sides.\r<BR>\n" );
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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;\" > Combine like terms.\r<BR>\n" );
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document.write( "Notice that the quadratic <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2000x%5E2-10000x%2B1000000 ALIGN=MIDDLE  ALT=\"-2000x%5E2-10000x%2B1000000\"   DISABLED_style= \"max-width:90%; height:auto;\" > is in the form of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Ax%5E2%2BBx%2BC ALIGN=MIDDLE  ALT=\"Ax%5E2%2BBx%2BC\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=-2000 ALIGN=MIDDLE  ALT=\"A=-2000\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B=-10000 ALIGN=MIDDLE  ALT=\"B=-10000\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=1000000 ALIGN=MIDDLE  ALT=\"C=1000000\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Let's use the quadratic formula to solve for \"x\":\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 ALIGN=MIDDLE  ALT=\"x+=+%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=x+=+%28-%28-10000%29+%2B-+sqrt%28+%28-10000%29%5E2-4%28-2000%29%281000000%29+%29%29%2F%282%28-2000%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=-2000 ALIGN=MIDDLE  ALT=\"A=-2000\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B=-10000 ALIGN=MIDDLE  ALT=\"B=-10000\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=1000000 ALIGN=MIDDLE  ALT=\"C=1000000\"   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=x+=+%2810000+%2B-+sqrt%28+%28-10000%29%5E2-4%28-2000%29%281000000%29+%29%29%2F%282%28-2000%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Negate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-10000 ALIGN=MIDDLE  ALT=\"-10000\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10000 ALIGN=MIDDLE  ALT=\"10000\"   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=x+=+%2810000+%2B-+sqrt%28+100000000-4%28-2000%29%281000000%29+%29%29%2F%282%28-2000%29%29 ALIGN=MIDDLE  ALT=\"x+=+%2810000+%2B-+sqrt%28+100000000-4%28-2000%29%281000000%29+%29%29%2F%282%28-2000%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-10000 ALIGN=MIDDLE  ALT=\"-10000\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100000000 ALIGN=MIDDLE  ALT=\"100000000\"   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=x+=+%2810000+%2B-+sqrt%28+100000000--8000000000+%29%29%2F%282%28-2000%29%29 ALIGN=MIDDLE  ALT=\"x+=+%2810000+%2B-+sqrt%28+100000000--8000000000+%29%29%2F%282%28-2000%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%28-2000%29%281000000%29 ALIGN=MIDDLE  ALT=\"4%28-2000%29%281000000%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-8000000000 ALIGN=MIDDLE  ALT=\"-8000000000\"   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=x+=+%2810000+%2B-+sqrt%28+100000000%2B8000000000+%29%29%2F%282%28-2000%29%29 ALIGN=MIDDLE  ALT=\"x+=+%2810000+%2B-+sqrt%28+100000000%2B8000000000+%29%29%2F%282%28-2000%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28100000000--8000000000%29 ALIGN=MIDDLE  ALT=\"sqrt%28100000000--8000000000%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28100000000%2B8000000000%29 ALIGN=MIDDLE  ALT=\"sqrt%28100000000%2B8000000000%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=x+=+%2810000+%2B-+sqrt%28+8100000000+%29%29%2F%282%28-2000%29%29 ALIGN=MIDDLE  ALT=\"x+=+%2810000+%2B-+sqrt%28+8100000000+%29%29%2F%282%28-2000%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100000000 ALIGN=MIDDLE  ALT=\"100000000\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8000000000 ALIGN=MIDDLE  ALT=\"8000000000\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8100000000 ALIGN=MIDDLE  ALT=\"8100000000\"   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=x+=+%2810000+%2B-+sqrt%28+8100000000+%29%29%2F%28-4000%29 ALIGN=MIDDLE  ALT=\"x+=+%2810000+%2B-+sqrt%28+8100000000+%29%29%2F%28-4000%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=-2000 ALIGN=MIDDLE  ALT=\"-2000\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4000 ALIGN=MIDDLE  ALT=\"-4000\"   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=x+=+%2810000+%2B-+90000%29%2F%28-4000%29 ALIGN=MIDDLE  ALT=\"x+=+%2810000+%2B-+90000%29%2F%28-4000%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=8100000000 ALIGN=MIDDLE  ALT=\"8100000000\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=90000 ALIGN=MIDDLE  ALT=\"90000\"   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=x+=+%2810000+%2B+90000%29%2F%28-4000%29 ALIGN=MIDDLE  ALT=\"x+=+%2810000+%2B+90000%29%2F%28-4000%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2810000+-+90000%29%2F%28-4000%29 ALIGN=MIDDLE  ALT=\"x+=+%2810000+-+90000%29%2F%28-4000%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=x+=+%28100000%29%2F%28-4000%29 ALIGN=MIDDLE  ALT=\"x+=+%28100000%29%2F%28-4000%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=++%28-80000%29%2F%28-4000%29 ALIGN=MIDDLE  ALT=\"x+=++%28-80000%29%2F%28-4000%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=x+=+-25 ALIGN=MIDDLE  ALT=\"x+=+-25\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+20 ALIGN=MIDDLE  ALT=\"x+=+20\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify. \r<BR>\n" );
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document.write( "So the <i>possible</i> answers are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-25 ALIGN=MIDDLE  ALT=\"x+=+-25\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+20 ALIGN=MIDDLE  ALT=\"x+=+20\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "However, a negative number of people doesn't make any sense. So we must ignore the solution <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-25 ALIGN=MIDDLE  ALT=\"x=-25\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So the solution is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+20 ALIGN=MIDDLE  ALT=\"x+=+20\"   DISABLED_style= \"max-width:90%; height:auto;\" > which means that there are 20 members currently in the club (before the 5 people join). </SPAN>\n" );
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