Arectangular auditorium seats 1702 people. the number of seats in each row exceeds the number of rows by 9. find the number of seats in each row.

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.

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