Extra Credit! If 18 students occupy 3/5of the seats in the classroom, how many students would occupy 2/3 of the seats in the room?

Answer 1

Let's start by determining the total number of seats in the classroom. Given that 18 students occupy \( \frac{3}{5} \) of the seats, we can set up the equation:

\[
18 = \frac{3}{5} \times \text{total seats}
\]

Let \( S \) represent the total number of seats. Then,

\[
18 = \frac{3}{5} S
\]

To find \( S \), we need to solve for \( S \) by isolating it on one side of the equation. Multiply both sides by the reciprocal of \( \frac{3}{5} \):

\[
S = 18 \times \frac{5}{3}
\]

Calculate the right side:

\[
S = 18 \times \frac{5}{3} = 18 \times \frac{5}{3} = \frac{18 \cdot 5}{3} = \frac{90}{3} = 30
\]

Thus, the total number of seats in the classroom is 30.

Next, we want to find out how many students would occupy \( \frac{2}{3} \) of the seats. We set up the following expression:

\[
\text{Number of students} = \frac{2}{3} \times \text{total seats}
\]

Substitute \( S = 30 \):

\[
\text{Number of students} = \frac{2}{3} \times 30
\]

Calculate the above expression:

\[
\text{Number of students} = \frac{2 \cdot 30}{3} = \frac{60}{3} = 20
\]

Therefore, 20 students would occupy \( \frac{2}{3} \) of the seats in the room.

Answer 2

is 20 or 12

Answer 3

Let's verify the calculations again to ensure accuracy.

We already determined the total number of seats in the classroom as 30.

Given that we need to find how many students would occupy \(\frac{2}{3}\) of these seats, we set up the expression:

\[
\text{Number of students} = \frac{2}{3} \times 30
\]

Calculate the above expression:

\[
\frac{2}{3} \times 30 = \frac{2 \cdot 30}{3} = \frac{60}{3} = 20
\]

The calculation is correct. Therefore, 20 students would occupy \(\frac{2}{3}\) of the seats in the room.

So the correct answer is 20 students.