To determine how many students would occupy \( \frac{2}{3} \) of the seats in the classroom, we first need to calculate the total number of seats.
Since 18 students occupy \( \frac{3}{5} \) of the seats, we can set up the following equation to find the total number of seats, denoted as \( S \):
\[ \frac{3}{5} S = 18 \]
To find \( S \), we can solve for it by multiplying both sides by \( \frac{5}{3} \):
\[ S = 18 \times \frac{5}{3} = 18 \times \frac{5}{3} = 30 \]
Now that we know the total number of seats in the classroom is 30, we can find how many students would occupy \( \frac{2}{3} \) of the seats.
Calculating \( \frac{2}{3} \) of the total seats:
\[ \frac{2}{3} \times 30 = 20 \]
Therefore, if 20 seats are occupied, the number of students that would occupy \( \frac{2}{3} \) of the seats in the classroom is \( \boxed{20} \).
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