Question

A middle school took all of its 6th grade students on a field trip to see a symphony. The students filled 1859 seats, leaving 35% vacant. How many total seats were in the theater?

Answer 1

Let \( x \) be the total number of seats in the theater.

Given that 35% of the seats were vacant, that means 65% of the seats were filled by the students. We know that the students filled 1859 seats, so we can set up the equation:

\[
0.65x = 1859
\]

To find \( x \), we divide both sides of the equation by 0.65:

\[
x = \frac{1859}{0.65}
\]

Now we can perform the division:

\[
x = 2853.846153846153846
\]

Since the number of seats must be a whole number, we round this to the nearest whole number:

\[
x = 2854
\]

Now, let’s confirm that this answer is consistent with the information given. First, we check 35% of the total number of seats:

\[
0.35 \times 2854 = 999.9 \approx 1000
\]

Then we verify how many seats were filled:

\[
0.65 \times 2854 = 1859.1 \approx 1859
\]

This verifies that both calculations are consistent with the problem statement.

Thus, the total number of seats in the theater is

\[
\boxed{2854}
\]