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# A rectangular auditorium seats 2120 people. The number of seats in each row exceeds the number of rows by 13 . Find the number of seats in each row.

how do I do this? I have no idea what to do at al!!!

### 1 Answer by Expert Tutors

John M. | High School and College Science TutorHigh School and College Science Tutor
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Let's look at the situation.  This auditorium has rows of seats, and since it is rectangular, each row will have the same number of seats.  So if we multiply the number of rows by the number of seats in each row, it will give us the total number of seats.  It's similar to multiplying the length by the width of a rectangle to get the area.

Let's say there are x rows.  Since the number of seats in each row exceeds the number of rows by 13, there would be x+13 seats in each row.  The total number of seats is 2120, so

x(x+13) = 2120

x2 + 13x = 2120

x2 + 13x - 2120 = 0

We can either use the quadratic equation or factoring

(x+53)(x-40) = 0

x = -53, 40

Since we can't have a negative number of rows, there are 40 rows with 53 seats in each row.