Question

the total number of seats in an auditorium is modeled by f(x) = 2x² - 24x where x represents the number of seats in each row how many seats are there in each row if it has a total of 1280 seats ?A) 32B) 108C)20 D) 640

Answer 1

SOLUTION

We want to find how many seats are in each row, using the model given.

Note that the number of seats in a row is given as x,

hence the total number of seats becomes f(x).

So form the model

$\begin{gathered} f\mleft(x\mright)=2x^{2}-24x \\ f(x)=1280 \\ so, \\ 2x^{2}-24x=1280 \\ 2x^{2}-24x-1280=0 \end{gathered}$

Solving for x, we have

$\begin{gathered} 2x^{2}-24x-1280=0 \\ \text{dividing through by 2, we have } \\ \frac{2x^2}{2}-\frac{24x}{2}-\frac{1280}{2}=\frac{0}{2} \\ x^2-12x-640=0 \\ x^2-32x+20x-640=0 \\ x(x-32)+20(x-32)=0 \\ (x+20)(x-32)=0 \\ x+20=0 \\ x=-20 \\ OR \\ x-32=0 \\ x=32 \end{gathered}$

Since the number of seats cannot be a negative number, that is -20,

hence the answer is 32, Option A