Instead of using letters from A to AA, let's use numbers. Also, let's number the rows from 0 to 26. So, our labelling will go like this:
The reason for this labelling is the following: we know that row A has 9 seats, and the following rows have three more seats than the previous one. Let's build a table like the previous one, containing the number of seats for the first few rows:
So, as you can see, the -th row has exactly
more seats than the first one.
So, we have the following sequence:
Which defines the number of seats for each row.
Answering the questions is now easy: the 27 row, AA, is the 26th term in our sequence:
The total number of seats is the sum of all the terms in the sequence:
Finally, let be the number of adult tickets, and
be the number of student tickets. We know that twice as many student tickets were sold as adult tickets, so we have
Since the show was a sold out, we have
So, 432 adult tickets were sold, which implies that
student tickets were sold. Let be the cost of a student ticket. Adult tickets then cost
, and the total revenue is
So, we have