SOLUTION: 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 th
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Question 184367: 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?
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?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
"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 n be the total number of karate students. Then 
is the number of 7th graders. \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 n. So:
\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
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