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We have been given that a rectangular auditorium seats 1702 people. Also, the number of seats in each row exceeds the number of rows by 9.
Let us assume that there are x rows in the auditorium. Therefore, there must be (x+9) seats in the each row. This will also be equal to the number of columns in the auditorium.
Therefore, we can set up an equation as:
We can now factor this quadratic as shown below:
Upon solving this equation, we get:
Since number of rows cannot be negative. Therefore, there must be 37 rows in the auditorium. And hence, the number of seats in each row will be 37+9=46 seats.