Question

A theater can seat 957 people. The number of rows is 4 less than the number of seats in each row. How many rows of seats are there?

Answer 1

The answer is: 29 rows of seats.

The explanation is shown below:

1. Let's call
`x` the number of seats in a row.

2. You have that the number of rows is 4 less than the number of seats in each row (
`x-4`).

3. The total seats, which is 957, is obtained by multiplying the number of seats in a row by the numbers of rows. Therefore, you can write the following expression:

`x(x-4)=957\\x^(2)-4x-957=0`

4. Solve for
`x`. You can use the Quadratic formula, which is:

`x=\frac{-b+/-\sqrt{b^(2)-4ac}}{2a}`

Where:

`a=1\\b=-4\\c=-957`

5. Substitute values:

`x=\frac{-(-4)+/-\sqrt{(-4)^(2)-4(1)(-957)}}{2(1)}\\x_1=33\\x_2=-29`

6. You must choose the positive value. Therefore, the number of rows of seats is:

`x-4=33-4=29`