Question

A rectangular auditorium seats 2709 people. The number of seats in each row exceeds the number of rows by 20. Find the number of seats in each row.

Answer 1

Let the number of rows = x
Then,
number of seats in each row = x + 20

Total seats = x*(x+20)
So,
x*(x+20) = 2709
x^2 + 20x - 2709 = 0

This is quadratic equation (ax^2+bx+c=0)
a = 1
b = 20
c = -2.709*10^3

Roots can be found by
x = {-b + sqrt(b^2-4*a*c)}/2a
x = {-b - sqrt(b^2-4*a*c)}/2a

b^2-4*a*c = 1.124*10^4

roots are :
x = 43 and x = -63

since x can't be negative, the possible value of x is
x = 43

number of seats in each row = x + 20
= 43 + 20
= 63
Answer: 63