A rectangular auditorium seats 1960 people. The number of seats in each row exceeds the number of rows by 9. Find the number of seats in each row.

Question

Thanks!

Answer 1

Ah, but divide by what? If there are r rows, each row has r+9 seats. So,

r(r+9) = 1960
r^2+9r-1960 = 0
factors of 1960 are many, but two which differ by 9 are 40 and 49. So,
(r+49)(r-40) = 0

There are 40 rows of 49 seats.