Question

An auditorium in a local high school contains 475 seats. There are 6 fewer rows than the number of seats per row. Find the number of rows and the number of seats per row.

Answer 1

The number of seats per row is 25 and the number of rows is 19.

Step-by-step explanation:

Let x be the number of seats per row.

Since there are 6 fewer rows than the number of seats per row, the number of rows can be represented as (x - 6).

We know that the total number of seats is 475, so we can set up the equation:

(x - 6) * x = 475

Simplifying the equation, we get:

x² - 6x - 475 = 0

We can solve this quadratic equation by factoring or using the quadratic formula. Let's use factoring:

(x - 25)(x + 19) = 0

Setting each factor equal to zero, we find two possible values for x: x = 25 or x = -19. Since the number of seats cannot be negative, we discard x = -19.

Therefore, the number of seats per row is 25, and the number of rows is (25 - 6) = 19.