Question

A theater can seat 120 people. The number of rows is 7 less than the number of seats in each row. How many rows of seats are there?

Answer 1

Let x be the number of rows.

If the number of rows is 7 less than the number of seats in each row, then the number of seats in a row is x+7. The total number of seats is

x·(x+7).

You know that a theater can seat 120 people, then

x·(x+7)=120.

Solve it:

$x^2+7x-120=0,\\\\D=7^2-4\cdot (-120)=49+480=529,\ \sqrt{D}=23,\\\\x_1=\dfrac{-7+23}{2}=8, \ x_2=\dfrac{-7-23}{2}=-15.$

The number of rows must be positive, then x=8.

Answer: there are 8 rows with 15 seats at each.