Answer:
Let's use algebra to solve this problem. Let "x" represent the number of seats in each row. According to the information given, the number of rows is 5 less than the number of seats in each row, so the number of rows can be represented as "x - 5."
Since the theater can seat 300 people, we can set up the equation:
Number of rows (x - 5) multiplied by Number of seats in each row (x) = 300
Now, we can solve for x:
(x - 5) * x = 300
x^2 - 5x = 300
Now, let's rearrange the equation:
x^2 - 5x - 300 = 0
We have a quadratic equation. To solve for x, you can use the quadratic formula:
x = (-b ± √(b² - 4ac)) / (2a)
In this equation, a = 1, b = -5, and c = -300. Plugging in these values, we get:
x = (5 ± √((-5)² - 4 * 1 * (-300))) / (2 * 1)
x = (5 ± √(25 + 1200)) / 2
x = (5 ± √1225) / 2
x = (5 ± 35) / 2
Now, we have two possible solutions:
1. x = (5 + 35) / 2 = 40 / 2 = 20
2. x = (5 - 35) / 2 = -30 / 2 = -15
Since the number of seats in each row cannot be negative, we take the positive solution:
x = 20
So, there are 20 seats in each row, and the number of rows is:
Number of rows = x - 5 = 20 - 5 = 15
There are 15 rows of seats in the theater.