document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=213451>Question 213451</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a social club charters a plane at a cost of $42240 to take a group of members on an excursion to atlantic city. at the last minute, 8 people in the group decide not to go. this raises the transportation cost per person by $22. how many people originally intended to take the trip? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #161239 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=161239\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x = number of people who were going to attend.<BR>\n" );
document.write( "x-8 = number of people who eventually attended.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "y = original cost per person = 42240/x.<BR>\n" );
document.write( "multiply both sides of this by x to get:<BR>\n" );
document.write( "x*y = 42240.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "y+22 = increased cost per person = 42240/(x-8).<BR>\n" );
document.write( "multiply both sides of this by (x-8) to get:<BR>\n" );
document.write( "(x-8)*y = 42240.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "since they both equal 42240, we have:<BR>\n" );
document.write( "x*y = (x-8)*(y+22)<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "we remove parentheses on the right side of this equation to get:<BR>\n" );
document.write( "xy = xy + 22x -8y - 176<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "we subtract xy from both sides of this equation to get:<BR>\n" );
document.write( "0 = 22x - 8y - 176<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "we add 8y to both sides of this equation to get:<BR>\n" );
document.write( "8y = 22x - 176<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "we divide both sides of this equation to get:<BR>\n" );
document.write( "y = (22x - 176)/8<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "we substitute in the equation xy = 42240 to get:<BR>\n" );
document.write( "x * (22x-176)/8 = 42240<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "we multiply both sides of this equation by 8 to get:<BR>\n" );
document.write( "x * (22x - 176) = 42240 * 8<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "we remove parentheses to get:<BR>\n" );
document.write( "22x^2 - 176x = 42240 * 8<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "we divide both sides of this equation by 22 to get:<BR>\n" );
document.write( "x^2 - 8x = 15360<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "we place this equation into standard quadratic equation form of ax^2 + bx + c = 0 by subtracting 15360 from both sides of this equation to get:<BR>\n" );
document.write( "x^2 - 8x - 15360 = 0<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "a = 1<BR>\n" );
document.write( "b = -8<BR>\n" );
document.write( "c = -15360<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "possible factors to get a c factor of 15360 are:<BR>\n" );
document.write( "15360 * 1<BR>\n" );
document.write( "7680 * 2<BR>\n" );
document.write( "3840 * 4<BR>\n" );
document.write( "1920 * 8<BR>\n" );
document.write( "960 * 16<BR>\n" );
document.write( "480 * 32<BR>\n" );
document.write( "240 * 64<BR>\n" );
document.write( "120 * 128<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "of these 120 * 128 is the most promising because 128 minus 120 = 8 which is our b factor.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "our possible factors for this quadratic equation are:<BR>\n" );
document.write( "(x-128) * (x+120) = 0<BR>\n" );
document.write( "we multiply these factors out to get:<BR>\n" );
document.write( "x*x = x^2<BR>\n" );
document.write( "x*120 = 120x<BR>\n" );
document.write( "-128*x = -128x<BR>\n" );
document.write( "-128*120 = -15360<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "We add these together and combine like terms to get:<BR>\n" );
document.write( "x^2 - 8x - 15360 = 0<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "since this is identical to our quadratic equation, we have the right factors.<BR>\n" );
document.write( "x = 128 or x = -120<BR>\n" );
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document.write( "x can't be -120 because then the number of persons would be negative.<BR>\n" );
document.write( "x has to be 128.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "the original number in the party is 128.<BR>\n" );
document.write( "the cost per person would have been 42240/128 = $330.<BR>\n" );
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document.write( "the new number in the party is 128 - 8 = 120.<BR>\n" );
document.write( "the new cost per person is 42240/120 = $352.<BR>\n" );
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document.write( "$352 - $330 = $22 which is the increas in cost per person.<BR>\n" );
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document.write( "Your answer is:<BR>\n" );
document.write( "128 people originally intended to take the trip.<BR>\n" );
document.write( "----- </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );