document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=335954>Question 335954</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A group of math teachers went to a restaurant. They agreed to split the bill equally. When the bill arrived, two of them discovered they had forgotten their money. The others agreed to make up the difference by paying an extra $1.30 each. If the total bill was $78, how many teachers were in the group? \r<BR>\n" );
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document.write( "I figured out the answer is 12 teachers but i can't figure out the equation. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #240935 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=240935\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A group of math teachers went to a restaurant. <BR>\n" );
document.write( "They agreed to split the bill equally. <BR>\n" );
document.write( "When the bill arrived, two of them discovered they had forgotten their money. The others agreed to make up the difference by paying an extra $1.30 each. If the total bill was $78, how many teachers were in the group?<BR>\n" );
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document.write( "Let x be the expected number payers.<BR>\n" );
document.write( "Average charge would be 78/x.<BR>\n" );
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document.write( "x-2 actually shared the bill.<BR>\n" );
document.write( "Average charge would be 78/(x-2)<BR>\n" );
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document.write( "Equation:<BR>\n" );
document.write( "New average - old average = 1.30<BR>\n" );
document.write( "78/(x-2) - 78/x = 1.30<BR>\n" );
document.write( "Multiply thru by x(x-2) to get:<BR>\n" );
document.write( "78x -78(x-2) = 1.3x(x-2)<BR>\n" );
document.write( "78*2 = 1.3x^2 - 2.6x<BR>\n" );
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document.write( "Multiply thru by 10 to get rid of the decimals:<BR>\n" );
document.write( "13x^2 - 26x - 1560 = 0<BR>\n" );
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document.write( "x^2 - 2x - 120 = 0<BR>\n" );
document.write( "(x-12)(x+10) = 0<BR>\n" );
document.write( "Positive solution:<BR>\n" );
document.write( "x = 12 (original number of payers before 2 reneged)<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "============ \r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );