Final answer:
After setting up an algebraic equation, we find that there are 23 rows of seats in the theater by finding factors of 621 that differ by 4, which are 23 (the number of rows) and 27 (the number of seats in each row).
Step-by-step explanation:
The question presented is a problem that can be solved using algebra to find the number of rows in a theater. Let's denote the number of rows as r and the number of seats in each row as r + 4. Since the total number of seats in the theater is 621, the equation to represent the situation is r * (r + 4) = 621.
To solve the quadratic equation, we look for factors of 621 that have a difference of 4. After a bit of trial and error, we find that 23 and 27 are such factors. Thus, r = 23 (the number of rows) since the number of rows is 4 less than the number of seats in each row.
Therefore, there are 23 rows of seats in the theater.