Question

A rectangle auditorium seats 1260 people. The number of seats in each row exceeds the number of rows by 12. Find the number of seats in each row

Answer 1

The number of seats in each row of the rectangle auditorium is 42.

Step-by-step explanation:

Let's represent the number of rows as x.

We know that the number of seats in each row exceeds the number of rows by 12. So the number of seats in each row can be represented as x + 12.

We are given that the total number of seats is 1260, so we can set up the equation:

x * (x + 12) = 1260

By factoring the equation, we get:

x^2 + 12x - 1260 = 0

Now we can solve this quadratic equation by factoring or using the quadratic formula. By factoring, we have:

(x + 42)(x - 30) = 0

So x could be either -42 or 30. Since the number of rows cannot be negative, we can ignore the -42 solution.

Therefore, the number of seats in each row is 30 + 12 = 42.