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:

$x-4=33-4=29$