Question

A middle school took all of its 6th grade students on a field trip to see a ballet. The students filled 702 seats, leaving 35% vacant. How many total seats were in the theater?

Answer 1

Let \( x \) represent the total number of seats in the theater. According to the problem, 35% of the seats were vacant, meaning that 65% of the seats were filled by the 6th grade students.

We can express this relationship mathematically:
\[
0.65x = 702
\]

To find \( x \), we can solve the equation by dividing both sides by 0.65:
\[
x = \frac{702}{0.65}
\]

Now, performing the division:
\[
x = 1080
\]

Thus, the total number of seats in the theater is \( \boxed{1080} \).