Asked by Jeannie
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.
Answers
Answered by
Lena
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.
# 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.
Answered by
Lena
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.
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