document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=166061>Question 166061</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 10.2 94) sharing cost: The members of a flying club plan to share equally the cost of $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 #122359 by </B><A HREF=/tutors/aboutme.mpl?userid=gonzo><B>gonzo(654)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=gonzo><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=122359\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let P = number of people in the club.<BR>\n" );
document.write( "let C = Cost for each person<BR>\n" );
document.write( "let T = total cost = 200000<BR>\n" );
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document.write( "P*C = 200000 (equation 1)<BR>\n" );
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document.write( "add 5 people to split the cost and save 2000 per person<BR>\n" );
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document.write( "(P+5) * (C-2000) = 200000 (equation 2)<BR>\n" );
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document.write( "you have 2 equations to work with:<BR>\n" );
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document.write( "multiply out the second equation:<BR>\n" );
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document.write( "P*C - 2000*P + 5*C - 10000 = 200000<BR>\n" );
document.write( "since P*C equals 200000, then this equation also equals P*C<BR>\n" );
document.write( "equation becomes:<BR>\n" );
document.write( "P*C - 2000*P + 5*C - 10000 = P*C<BR>\n" );
document.write( "subtract P*C from both sides of the equation:<BR>\n" );
document.write( "-2000*P + 5*C - 10000 = 0<BR>\n" );
document.write( "add 2000*P + 10000 to both sides of the equation:<BR>\n" );
document.write( "5*C = 2000*P + 10000<BR>\n" );
document.write( "divide both sides of the equation by 5:<BR>\n" );
document.write( "C = 400*P + 2000<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "in equation 1, substitute 400*P + 2000 for C<BR>\n" );
document.write( "that equation becomes:<BR>\n" );
document.write( "P * (400*P + 2000) = 200000<BR>\n" );
document.write( "multiply out:<BR>\n" );
document.write( "400*P^2 + 2000*P = 200000<BR>\n" );
document.write( "divide both sides of equation by 400:<BR>\n" );
document.write( "P^2 + 5*P = 500<BR>\n" );
document.write( "subtract 500 from both sides of equation:<BR>\n" );
document.write( "P^2 + 5*P - 500 = 0<BR>\n" );
document.write( "solve the quadratic equation:<BR>\n" );
document.write( "(P+25) * (P-20) = 0<BR>\n" );
document.write( "roots are:<BR>\n" );
document.write( "P = -25<BR>\n" );
document.write( "or<BR>\n" );
document.write( "P = 20<BR>\n" );
document.write( "since the number of people can't be negative, P looks like it will be 20.<BR>\n" );
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document.write( "if P = 20, then P*C = 200000 becomes 20*C = 200000 which make C = 10000.<BR>\n" );
document.write( "likes like original number of people is 20 and original investment each is 10000 dollars.<BR>\n" );
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document.write( "P = number of original members = 20.<BR>\n" );
document.write( "C = original investment = 10000.<BR>\n" );
document.write( "add 5 new members and total members = 25.<BR>\n" );
document.write( "divide 200000 by 25 and you get 8000 investment each.<BR>\n" );
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document.write( "number of members is 5 more than original (20 + 5 = 25).<BR>\n" );
document.write( "amount of investment of each is 2000 less than original investment (10000 - 2000 = 8000).<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );