document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=201020>Question 201020</A>: <I><SPAN STYLE=\"word-break: break-all;\"> During a recent survey of 2 classes, 1/3 of the students bring their lunch to school, 1/4 buy their lunch, and 1/6 go home.  The remaining 18 students don't eat lunch.  How many students are in the 2 classes?\r<BR>\n" );
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document.write( "My niece answered 116.  Please verify if this correct, so I can double check our work, it has been several since my Algebra days.  Thanks, Cindy </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #151260 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=151260\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "Right off the bat you can tell that 116 is not correct.  116 is not evenly divisible by either 3 or 6, so you would have a fractional part of a student bringing their lunch and another fractional part of a student going home.  Basically, someone's head and shoulders went home and the rest of their body stayed at school and ate the lunch they brought.\r<BR>\n" );
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document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\"> represent the number of students in the two classes.  One third of them bring their lunch, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac{x}{3}\">, one fourth of them buy, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac{x}{4}\">, one-sixth go home, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac{x}{6}\">, and 18 don't eat lunch.  And the sum of all these pieces is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\">, so:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x = \frac{x}{3} + \frac{x}{4} + \frac{x}{6} + 18\">\r<BR>\n" );
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document.write( "The lowest common denominator of 3, 4, and 6 is 12, so multiply both sides of the equation by 12:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 12x = 4x + 3x + 2x + (12\cdot18)\"> \r<BR>\n" );
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document.write( "Collect terms:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 12x = 9x + (12\cdot18)\">\r<BR>\n" );
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document.write( "Add <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large -9x\"> to both sides:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 3x = 12\cdot18\">\r<BR>\n" );
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document.write( "Multiply both sides by <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac{1}{3}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x = 4\cdot18 = 72\">\r<BR>\n" );
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document.write( "Check the answer:  One-third of 72 is 24, one-fourth of 72 is 18, one-sixth of 72 is 12.  24 plus 18 plus 12 plus 18 is 72.  Answer checks.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
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