Question

A theater can seat 672 people. The number of rows is 4 less than the number of seats in each row. How many rows of seats are there?

Answer 1

24 rows of seats

let n be the number of rows

then the number of seats per row = n + 4

number of seats = number of rows × number of seats per row

n(n + 4 ) = 672

n² + 4n - 672 = 0 ← in standard form

the factors of - 672 which sum to + 4 are + 28 and - 24

(n + 28)(n - 24) = 0

equate each factor to zero and solve for n

n + 28 = 0 ⇒ n = - 28

n - 24 = 0 ⇒ n = 24

number of rows n > 0

number of rows = 24 and number of seats per row = 28

24 × 28 = 672 as a check