Question 184367
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"I know 1/3n is the 7th and 1/2(2/3n) is the sixth" has all the essential elements of the required equation.


Let <i>n</i> be the total number of karate students.  Then *[tex \Large \frac{n}{3}] is the number of 7th graders.  *[tex \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:


*[tex \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]



John
*[tex \Large e^{i\pi} + 1 = 0]
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