Question

A rectangular auditorium seats 1749 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

The total number of seats is given by:

Seats = (number of rows)*(seats per row)

Let r = the number of rows. We are told that the number of seats in each row exceeds the total number of rows (r) by 13. So the seats per row = r+13. Given that there are 3150 seats in total, we have:

3150 = r*(r+13)

3150 = r2 + 13r

0 = r2 + 13r - 3150

Factors to:

0 = (r-50)(r+63)

r = 50 and -63

Since we can't have -63 rows, the answer is r = 50 rows.

The number of seats per row = r + 13 = 50 + 13 = 63 seats per row.