To determine how many students would occupy \( \frac{2}{3} \) of the seats in the classroom, we first need to find the total number of seats based on how many students occupy \( \frac{3}{5} \) of the seats.
Given that 18 students occupy \( \frac{3}{5} \) of the seats, we can set up the following equation:
\[ \frac{3}{5} \text{ of total seats} = 18 \]
Let \( S \) represent the total number of seats in the classroom. We can express this relationship as:
\[ \frac{3}{5} S = 18 \]
To find \( S \), we can solve for it by isolating it in the equation:
\[ S = 18 \cdot \frac{5}{3} \]
Calculating that gives:
\[ S = 18 \cdot \frac{5}{3} = 6 \cdot 5 = 30 \]
Now, we know there are 30 total seats in the classroom. Next, we want to find out how many students would occupy \( \frac{2}{3} \) of the seats. We calculate \( \frac{2}{3} \) of the total number of seats:
\[ \frac{2}{3} S = \frac{2}{3} \cdot 30 \]
Calculating that:
\[ \frac{2}{3} \cdot 30 = 20 \]
Thus, 20 students would occupy \( \frac{2}{3} \) of the seats in the classroom.
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