document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=184367>Question 184367</A>: <I><SPAN STYLE=\"word-break: break-all;\"> One-third of the members on the karate team are in the seventh grade. Of the remaining team members, 50% are in sixth grade, and 12 are in eighth grade. How many students are on the karate team?\r<BR>\n" );
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document.write( "Logically I know 36 students: 12- 6th, 12- 7th and 12 8th. I know 1/3n is the 7th and 1/2(2/3N) is the sixth  How do I set it up in an equation to solve? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #138389 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=138389\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "\"I know 1/3n is the 7th and 1/2(2/3n) is the sixth\" has all the essential elements of the required equation.\r<BR>\n" );
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document.write( "Let <i>n</i> be the total number of karate students.  Then <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac{n}{3}\"> is the number of 7th graders.  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \left(\frac{1}{2}\right)\left(\frac{2}{3}\right)n\"> is the number of 6th graders.  12 is the number of 8th graders.  And finally, the sum of all three of these expressions must equal <i>n</i>.  So:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \ \ \frac{n}{3} + \left(\frac{1}{2}\right)\left(\frac{2}{3}\right)n + 12 = n \ \ \Rightarrow\ \ \frac{n}{3} + \frac{n}{3} + 12 = n   \ \ \Rightarrow\ \ \frac{n}{3} + \frac{n}{3} -n = -12 \ \ \Rightarrow\ \ -\frac{n}{3} = -12 \ \ \Rightarrow\ \ n = 36\">\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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