Question
If 18 students occupy `3/5`of the seats in the classroom, how many students would occupy `2/3` of the se
Answers
GPT-4o mini
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.
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.