A rectangular auditorium seats 900 people. The number of seats in each row exceeds the number of rows by 11. Find the number of seats in each row.

Answer 1

Total # of seats = 900
# of rows = R
# of seats = S

So according to the question, if we have R rows then we have R+11 seats

Total # of seats = # of rows * # of seats/row
900 = R * (R+11)
900 = R^2 + 11R
0 = R^2 + 11R -900
0 = (R+36)(R-25)

Therefore, you must have 25 rows with 36 seats in each row. We can't use -36 rows because it does not give us a realistic answer.

Answer 2

Essentially we've created a quadratic equation and we're solving it using factoring. If you don't understand how I solved this question, I can expand on my thinking. Let me know if it makes sense.