Sophomores

There are 3200 students at Lake High School, and 3/8 of these are sophomores. If 3/5 of the sophomores favor the school forming a crew team and 7/10 of the remaining students (not sophomores) are in favor of forming a crew team, how many students are opposed to this idea?

Correct answer:

x =  1080

Step-by-step explanation:

$$\begin{gathered} n=3200 \\ s=\frac{3}{8}\cdot n=\frac{3}{8}\cdot 3200=\frac{3\cdot 3200}{8}=\frac{9600}{8}=1200 \\ a=\frac{3}{5}\cdot s=\frac{3}{5}\cdot 1200=\frac{3\cdot 1200}{5}=\frac{3600}{5}=720 \\ b=(n-s)\cdot \frac{7}{10}=(3200-1200)\cdot \frac{7}{10}=1400 \\ x=n-a-b=3200-720-1400=1080 \end{gathered}$$

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