document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1167719>Question 1167719</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A group of friends hire a bus for a day for $480. At the last minute, two more people decide to go on the<BR>\n" );
document.write( "trip, and as a result each person pays $8 less. How many people went on 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 #792303 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=792303\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "the cost for the bus equals the number of people taking the bus times the amount that each person pays.\r<BR>\n" );
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document.write( "your equation is x * y = 480.\r<BR>\n" );
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document.write( "x is the number of people taking the bus and y is the amount that each person pays.\r<BR>\n" );
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document.write( "when you increase the number of people by 2 and reduce the price that each person pays by 8 dollars, then the formula becomes:\r<BR>\n" );
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document.write( "(x + 2) * (y - 8) = 480\r<BR>\n" );
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document.write( "in the first equation, solve for y to get y = 480 / x\r<BR>\n" );
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document.write( "in the second equation, replace y with 480 / x to get:\r<BR>\n" );
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document.write( "(x + 2) * (480 / x - 8) = 480\r<BR>\n" );
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document.write( "multiply both sides of this equation by x to get:\r<BR>\n" );
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document.write( "x * (x + 2) * (480 / x - 8) = 480 * x\r<BR>\n" );
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document.write( "simplify by multiplying x * (480/x - 8) to get:\r<BR>\n" );
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document.write( "(x + 2) * (480 - 8x) = 480 * x\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "480 * x - 8x^2 + 960 - 16x = 480 * x\r<BR>\n" );
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document.write( "subtract 480 * x from both sides of the equation to get:\r<BR>\n" );
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document.write( "-8x^2 + 960 - 16x = 0\r<BR>\n" );
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document.write( "order by descending order of degree to get:\r<BR>\n" );
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document.write( "-8x^2 - 16x + 960 = 0\r<BR>\n" );
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document.write( "divide both sides of the equation by 8 to get:\r<BR>\n" );
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document.write( "-x^2 - 2x + 120 = 0\r<BR>\n" );
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document.write( "multiply both sides of the equation by -1 to get:\r<BR>\n" );
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document.write( "x^2 + 2x - 120 = 0\r<BR>\n" );
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document.write( "factor this quadratic to get:\r<BR>\n" );
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document.write( "(x + 12) * (x - 10) = 0\r<BR>\n" );
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document.write( "solve for x to get:\r<BR>\n" );
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document.write( "x = -12 or x = 10\r<BR>\n" );
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document.write( "x can't be negative, so x = 10\r<BR>\n" );
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document.write( "x * y = 10 * y = 480<BR>\n" );
document.write( "solve for y to get:<BR>\n" );
document.write( "y = 48\r<BR>\n" );
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document.write( "(x + 2) * (y - 8) = 480 becomes:<BR>\n" );
document.write( "12 * 40 = 480<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "480 = 480\r<BR>\n" );
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document.write( "this confirms the solution is correct.\r<BR>\n" );
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document.write( "your solution is that 12 people went on the trip.\r<BR>\n" );
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document.write( "if 10 went, the price was 480 / 10 = 48 for each person.<BR>\n" );
document.write( "since 12 went, the price was 480 / 12 = 40 for each person.\r<BR>\n" );
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document.write( "each person paid 8 less.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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