document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=255012>Question 255012</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A grade 11 class, on a field trip to Montreal, had lunch in a restaurant. The bill came to $239.25. Four students had birthdays that day, and it was agreed that these four should not have to pay for lunch. The other students had to pay $1 more than if all students had paid. How many students had lunch?\r<BR>\n" );
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document.write( "I know that the answer is 33 children ate on the trip and that 29 paid.  The 29 that paid, had to pay 8.25 each.  If all the children paid then each would have paid 7.25.  I found this answer through trial and error, but can not find what the equation should be to get this answer.  If you could help I would be very greatful. Thanks so much. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #187357 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=187357\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> bill = $239.25\r<BR>\n" );
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document.write( "let x = number of students.\r<BR>\n" );
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document.write( "let y = amount each student paid.\r<BR>\n" );
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document.write( "if all students paid the bill, then:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=239.25+%2F+x+=+y ALIGN=MIDDLE  ALT=\"239.25+%2F+x+=+y\"   DISABLED_style= \"max-width:90%; height:auto;\" > (first equation)\r<BR>\n" );
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document.write( "if all but 4 paid the bill, then:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=239.25+%2F+%28x-4%29+=+y%2B1 ALIGN=MIDDLE  ALT=\"239.25+%2F+%28x-4%29+=+y%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > (second equation)\r<BR>\n" );
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document.write( "substitute for y in second equation by the value for y in first equation to get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=239.25+%2F+%28x-4%29+=+%28239.25%2Fx%29+%2B+1 ALIGN=MIDDLE  ALT=\"239.25+%2F+%28x-4%29+=+%28239.25%2Fx%29+%2B+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "you had one equation in 2 unknowns.   the substitution allows you to have 1 equation in 1 unknown.\r<BR>\n" );
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document.write( "multiply both sides of this equation by (x-4) to get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=239.25+=+%28x-4%29+%2A+%28%28239.25%2Fx%29+%2B+1%29 ALIGN=MIDDLE  ALT=\"239.25+=+%28x-4%29+%2A+%28%28239.25%2Fx%29+%2B+1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "multiply the factors to get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=239.25+=+239.25+%2B+x+-+4%2A%28239.25%2Fx%29+-+4 ALIGN=MIDDLE  ALT=\"239.25+=+239.25+%2B+x+-+4%2A%28239.25%2Fx%29+-+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "subtract 239.25 from both sides of the equation to get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+x+-+4%2A%28239.25%2Fx%29+-+4 ALIGN=MIDDLE  ALT=\"0+=+x+-+4%2A%28239.25%2Fx%29+-+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "remove parentheses to get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+x+-+%28957%29%2Fx+-+4 ALIGN=MIDDLE  ALT=\"0+=+x+-+%28957%29%2Fx+-+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "multiply both sides of equation by x to get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+x%5E2+-+957+-+4%2Ax ALIGN=MIDDLE  ALT=\"0+=+x%5E2+-+957+-+4%2Ax\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "rearrange terms to get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+4%2Ax+-+957+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+-+4%2Ax+-+957+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "use quadratic formula to solve for x to get:\r<BR>\n" );
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document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-%28-4%29+%2B-+sqrt%2816%5E2+-+%284%2A1%2A%28-957%29%29%29%29%2F%282%29 ALIGN=MIDDLE  ALT=\"%28-%28-4%29+%2B-+sqrt%2816%5E2+-+%284%2A1%2A%28-957%29%29%29%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "this becomes:\r<BR>\n" );
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document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284+%2B-+sqrt%2816%5E2+%2B+3828%29%29%2F%282%29 ALIGN=MIDDLE  ALT=\"%284+%2B-+sqrt%2816%5E2+%2B+3828%29%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > which becomes:\r<BR>\n" );
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document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284+%2B-+sqrt%283844%29%29%2F2 ALIGN=MIDDLE  ALT=\"%284+%2B-+sqrt%283844%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > which becomes:\r<BR>\n" );
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document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284+%2B-+62%29%2F2 ALIGN=MIDDLE  ALT=\"%284+%2B-+62%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > which becomes:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%284%2B62%29%2F2+=+66%2F2+=+33+ ALIGN=MIDDLE  ALT=\"x+=+%284%2B62%29%2F2+=+66%2F2+=+33+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "or:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%284-62%29%2F2+=+-58%2F2+=+-29 ALIGN=MIDDLE  ALT=\"x+=+%284-62%29%2F2+=+-58%2F2+=+-29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "since x has to be positive, then the solution narrows down to:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+33 ALIGN=MIDDLE  ALT=\"x+=+33\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "when 33 students pay the bill, the bill is $239.25 / 33 = $7.25 apiece.\r<BR>\n" );
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document.write( "when 29 students pay the bill (33-4 = 29), the bill is $239.25 / 29 = $8.25.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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