Quadratic word problems

Question

In a lecture hall there are 180 seats. The number of seats in each row is 8 more that the number of rows find the number of rows

Answer 1

Let x be the number of rows. The number of seats in each row is 8 more than the number of rows, so the number of seats per row is x+8. To get the total number of seats, multiply the number of rows times the number of seats per row. The total number of seats is 180:

x(x+8) = 180

x² + 8x = 180

x² + 8x - 180 = 0

Solve for x. It factors. You'll get two answers, one positive and one negative. Since you can't have a negative number of rows, choose the positive answer.