document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1207800>Question 1207800</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A group of 20 senior citizens can charter a bus for a one-day excursion trip for $15 per person. The charter company agrees to reduce the price of each ticket by 10¢ for each additional passenger in excess of 20 who goes on the trip, up to a maximum of 44 passengers (the capacity of the bus). If the final bill from the charter company was $482.40,how many seniors went on the trip, and how much did each pay?\r<BR>\n" );
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document.write( "This is too wordy for me to even know where to begin.<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 #845904 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13198)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=845904\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Unless you have a lot of experience, start by defining a variable.<br><BR>\n" );
document.write( "What does the problem ask for? It asks for the number of seniors who went on the trip.<br><BR>\n" );
document.write( "We could let x be the number who went on the trip.  But then the number of ADDITIONAL seniors, after the original 20, would be (x-20), which would complicate the solution process.<br><BR>\n" );
document.write( "Since the price per senior decreases by 10 cents for each ADDITIONAL senior....<br><BR>\n" );
document.write( "Let x = number of additional seniors<br><BR>\n" );
document.write( "The total cost of the trip, $482.40, is the product of the number of seniors and the cost for each.  Using our definition of x...<br><BR>\n" );
document.write( "20+x = number of seniors<BR>\n" );
document.write( "15-0.1x = cost per senior (writing 10 cents as 0.1 dollars)<br><BR>\n" );
document.write( "Then<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2820%2Bx%29%2815-0.1x%29=482.40 ALIGN=MIDDLE  ALT=\"%2820%2Bx%29%2815-0.1x%29=482.40\"   DISABLED_style= \"max-width:90%; height:auto;\" > [1]<br><BR>\n" );
document.write( "Expand using FOIL...<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=300-2x%2B15x-0.1x%5E2=482.40 ALIGN=MIDDLE  ALT=\"300-2x%2B15x-0.1x%5E2=482.40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-0.1x%5E2%2B13x%2B300=482.4 ALIGN=MIDDLE  ALT=\"-0.1x%5E2%2B13x%2B300=482.4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.1x%5E2-13x%2B182.4=0 ALIGN=MIDDLE  ALT=\"0.1x%5E2-13x%2B182.4=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-130x%2B1824=0 ALIGN=MIDDLE  ALT=\"x%5E2-130x%2B1824=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "This is an ugly quadratic equation that you could solve by factoring, by using the quadratic formula, or by using a tool like a graphing calculator.  Note that since a purely algebraic solution is not easy, the problem can probably be solved most quickly using a graphing calculator to solve equation [1] directly.<br><BR>\n" );
document.write( "In any case....<br><BR>\n" );
document.write( "Factoring gives<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-114%29%28x-16%29=0 ALIGN=MIDDLE  ALT=\"%28x-114%29%28x-16%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "So the number of additional seniors is either 114 or 16.  But since the capacity of the bus is 44, the correct number of additional seniors is 16.<br><BR>\n" );
document.write( "ANSWERS:<BR>\n" );
document.write( "number of seniors who went on the trip: 20+x = 20+16 = 36<BR>\n" );
document.write( "cost each: 15-0.1x =15-0.1(16) = $15.00-$1.60 = $13.40<BR>\n" );
document.write( "CHECK: 36($13.40) = $482.40<br><BR>\n" );
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