Question

Alright, here's one for Algebra:

The number of seats in a row has been increased at a rectangular-shape movie theater after renovation so that it is now five more than the total number of rows. How many rows are in in the theater, if its total seating capacity is 126 people now?

Answer 1

Let x= number rows
Then x + 5 = number of seats per row

x(x+5) = 126
X^2 + 5x = 126
x^2 + 5x -126 = 0; now factor or use quadratic:
(x+14)(x-9) = 0; so the answers are either -14, or 9, and since -14 is not possible in this case because you can't have a negative number of rows, the answer is 9 rows.

Check work: number of rows = 9, number of seats per row = 9+ 5= 14, and 9 x 14 = 126