The total number of seats in an auditorium is modeled by f(x) = 2x2 - 6x, where x represents the number of rows of seats. How many rows are there in the auditorium if it has a total of 416 seats?

Question

The total number of seats in an auditorium is modeled by f(x) = 2x2 - 6x, where x represents the number of rows of seats. How many rows are there in the auditorium if it has a total of 416 seats?

16

13

32

20

Answer 1

To find the number of rows in the auditorium, we need to solve the equation 2x^2 - 6x = 416.

Rearranging the equation, we get 2x^2 - 6x - 416 = 0.

Now, we can factor this quadratic equation as (2x + 26)(x - 16) = 0.

Setting each factor to zero, we get x = -26/2 (which is not a valid solution in the context of the problem) and x = 16.

Therefore, there are 16 rows in the auditorium if it has a total of 416 seats.