posted by lucy .
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.
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.