Question

The total number of seats in an auditorium is modeled by f(x) = 2x² - 12x, where x represents the number of rows of seats. How many rows are there in the auditorium if it has a total of 320 seats? Show work and explain how you got your answer

Answer 1

320 = 2x² - 12x as when there are an unknown number of rows there are 320 seats.
0 = 2x² - 12x - 320
0 = x² - 6x - 160
0 = (x - 16)(x + 10)
for this to = 0 one bracket must equal 0
therefore x = 16 or x = -10
not a negative number of rows.

Therefore must be 16.