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?

Answer 1

`f(x) = 2x^2 - 6x\\\\416 = 2x^2 - 6x\\\\0 = 2x^2 - 6x - 416\\\\(x - 16) (x + 13)\\\\x = 16    x = -13`

Since there can't be negative number of rows, the answer is 16.

Answer 2

Answer: The number of rows is 16.

Step-by-step explanation: Given that the total number of seats in an auditorium is modeled by the following equation:

`f(x)=2x^2-6x,`

where x represents the number of rows of seats.

We are to find the number of rows are there in the auditorium with a total of 416 seats.

So, we are to find the value of x if f(x) = 416.

We have

`2x^2-6x=416\\\\\Rightarrow x^2-3x=208\\\\\Rightarrow x^2-3x-208=0\\\\\Rightarrow x^2-16x+13x-208=0\\\\\Rightarrow x(x-16)+13(x-16)=0\\\\\Rightarrow (x-16)(x+13)=0\\\\\Rightarrow x-16=0~~~~~~~~~~x+13=0\\\\\Rightarrow x=16,~-13.`

Since the number of rows cannot be negative, so the required number of rows in the auditorium is 16.

Thus, the number f rows is 16.