Theater has 108 seats, which are arranged in rows. The number of seats in each row is 3 less than the number of rows. How many rows of seats are in the theater.

let the number of rows be n

then the number of seats in each row is n-3

n(n-3) = 108
n^2 - 3n - 108=0
(n-12)(n+ 9) = -
n = 12 or n = -9 , but we can't have a negative number of rows

there are 12 rows

Let's break down the information given:

Number of seats in each row = Number of rows - 3

So, we can form an equation based on the given information:

(Number of seats in each row) * (Number of rows) = Total number of seats in theater

Let's substitute the given values into the equation:

(Number of rows - 3) * (Number of rows) = 108

Expanding the equation:

Number of rows^2 - 3 number of rows = 108

Rearranging the equation to bring all terms to one side:

Number of rows^2 - 3 number of rows - 108 = 0

We now have a quadratic equation. To solve for the number of rows, we can use factoring or the quadratic formula. However, in this case, factoring is simpler:

(Number of rows + 9)(Number of rows - 12) = 0

From this, we can see that either the number of rows is -9 or 12. Since the number of rows cannot be negative, we discard -9.

Therefore, the number of rows in the theater is 12.

To find the number of rows in the theater, you need to set up an equation based on the given information. Let's call the number of rows "x".

According to the problem, the number of seats in each row is 3 less than the number of rows. So, the number of seats in each row would be (x - 3).

Since there are 108 seats in total, you can multiply the number of rows by the number of seats in each row to get the total number of seats.

So, the equation would be:
Total number of seats = Number of rows * Number of seats in each row
108 = x * (x - 3)

Now, you can solve this equation to find the value of "x", which represents the number of rows in the theater.