Question

In an auditorium, seats are arranged in rows and columns. the number of rows are equal to the number of seats in each row. when the number of rows are doubled and the number of seats in each row is reduced by 10, the total number of seats increases by 300.

if x is taken as number of row in original arrangement, write the quadratic equation that describes the situation ?

Answer 1

The quadratic equation that describes the situation where the number of rows and seats in an auditorium are altered, leading to an increase in total seats by 300, is x² - 20x - 300 = 0.

Step-by-step explanation:

In the original seating arrangement of an auditorium, the number of rows is equal to the number of seats in each row, which can be represented by x. When the number of rows is doubled (2x) and the number of seats in each row is reduced by 10 (x - 10), the total number of seats increases by 300. This situation can be described by a quadratic equation.

To write the quadratic equation, we start with the original number of seats which is x times x (or x²). After the changes, the total number of seats becomes 2x times (x - 10). The increase in the number of seats is given as 300, hence the equation can be set up as follows:

Original number of seats + 300 = New number of seats

x² + 300 = 2x(x - 10)

Expanding the right side and bringing all terms to one side to form a quadratic equation gives:

x² + 300 = 2x² - 20x

0 = 2x² - 20x - x² - 300

0 = x² - 20x - 300

Thus, the quadratic equation that describes the situation is x² - 20x - 300 = 0.