document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=209245>Question 209245</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A group of teenagers wanted to hire a small bus for their prom and they split the $600 total cost equally.  If they had had 5 fewer people, each person would have paid $10 more.  How many teenagers were there and how much did they each pay?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #158181 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=158181\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let x = number of teenagers.<BR>\n" );
document.write( "cost of the bus $600.00<BR>\n" );
document.write( "let c = cost per teenager.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "formula to determine cost per teenager is c = $600/x<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "if there were 5 less teenagers, the cost per teenager would have been $10 more.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "formula to determine cost per teenager when there is 5 less teenagers is:<BR>\n" );
document.write( "c + 10 = $600 / (x-5)<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "subtract 10 from this formula to get:<BR>\n" );
document.write( "c = ( $600 / (x-5) ) - $10<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "we have 2 formulas, each being equal to c so they are equal to each other.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "600 / x = ( 600 / (x-5) ) - 10<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "multiply both sides of this equation by (x) * (x-5) to get:<BR>\n" );
document.write( "600 * (x-5) = 600 * x - (10 * x * (x-5))<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "this become:<BR>\n" );
document.write( "( 600 * x ) - 3000 = ( 600 * x ) - ( 10 * x^2 ) + ( 50 * x )<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "subtract everything on the right hand side of this equation from both sides of this equation to get:<BR>\n" );
document.write( "(600*x) - 3000 - (600*x) + (10*x^2) - (50*x) = 0<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "combine like terms to get:<BR>\n" );
document.write( "10x^2 - 50x - 3000 = 0<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "divide both sides of this equation by 10 to get:<BR>\n" );
document.write( "x^2 - 5x - 300 = 0<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "this factors out to be:<BR>\n" );
document.write( "(x-20) * (x+15) = 0<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "x = 20<BR>\n" );
document.write( "or:<BR>\n" );
document.write( "x = -15<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "x has to be positive so the only possible solution is x = 20<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "plug x = 20 into the original equations:<BR>\n" );
document.write( "c = $600/x becomes c = $600/20 becomes c = $30.00<BR>\n" );
document.write( "c+$10 = $600/(x-5) becomes c+$10 = $600/15 becomes c+$10 = $40 becomes c = $30.00<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "your problem was:<BR>\n" );
document.write( "A group of teenagers wanted to hire a small bus for their prom and they split the $600 total cost equally.  If they had had 5 fewer people, each person would have paid $10 more.  How many teenagers were there and how much did they each pay? <BR>\n" );
document.write( "-----<BR>\n" );
document.write( "answer is:<BR>\n" );
document.write( "there were 20 teenagers there and the bus cost them $30.00 apiece.<BR>\n" );
document.write( "-----\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );