An auditorium contains 240 seats. The number of seats per row is four less than twice the number of rows. Find the number of rows and the number of seats per row.

Answer 1

Hi Katie,

Let' s use the variable, r , to represent the number of rows in the auditorium.

Since the number of seats in each row is equal to 4 less than twice the number of rows, we can write the following expression to show this: (2r - 4)

Next, the total number of seats is 240 and can also be calculated by multiplying the number of rows (r) by the number of seats in each row. We can write the following equation to show this:

r (2r - 4 ) = 240

Now we can solve this equation for r (positive solution only):

r (2r - 4 ) = 240

2r² -4r = 240

2r² -4r - 240 = 0

2(r² -2r - 120) = 0

2 (r -12) (r + 10) = 0

r = 12

There will be 12 rows.

Each row will have 2r - 4 seats or 2 • 12 - 4 =20

There will be 20 seats in each row.

NOTE: 12 rows • 20 seats = 240 total seats