Question

The seats in a theater are arranged in parallel rows that form a rectangular region. The number of seats in each row of the theater is 16 fewer than the number of rows. How many seats are in each row of a 1161-seat theater?

I have no idea how to solve this problem. Please help if you can! Thank you! :-)

Answer 1

n rows
(n-16) seats/row
n * (n-16) = 1161
n^2 - 16 n - 1161 = 0
well, I want factors of 1161 that differ by 16. I know sqrt 1161 = 34.07... so I geuss that around 27 would be a good guess and 27+16 = 43 and sure enough 43*27 = 1161
so
(n-43)(n+27) = 0
n = 43
and the number of seats per row = n-16 = 27

Answer 2

Let R = the number of rows.
Let Sb = the number of seats in each row

The seats in the theater are arranged in parallel rows that form a rectangular region.

Then, from "The number of seats in each row of the theater is 16 fewer than the number of rows" or Sb = R - 16.

The total number of seats is given by {Sr(R) = 1161

Therefore, Sr = R - 16 = 1161/R.

I leave the hard part for you.