Miss competition

How many girls took part in the Miss School competition if the ninth graders made up half of the contestants, two-thirds of the remaining girls were from eighth grade, and three were from seventh grade?

Final Answer:

n =  18

Step-by-step explanation:

$$\begin{gathered} n/2+2/3(n-n/2)+3=n \\ n/2+2/3\cdot (n-n/2)+3=n \\ n=18 \\ \text{ Verifying Solution: } \\ a=n/2=18/2=9 \\ b=\frac{2}{3}\cdot (n-a)=\frac{2}{3}\cdot (18-9)=6 \\ c=3 \\ s=a+b+c=9+6+3=18 \end{gathered}$$

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