Question

A car dealership manager has determined that the profit, in thousands of dollars, of the dealership can be determined by the expression LaTeX: x^2-4xL a T e X : x 2 − 4 x, where LaTeX: xL a T e X : x is the number of cars sold. A different manager states that the profit of the dealership can be determined by the function LaTeX: 5xL a T e X : 5 x. What number of cars sold makes the equation LaTeX: x^2-4x=5xL a T e X : x 2 − 4 x = 5 x true? Select all that apply.

Answer 1

The number of cars that brings the same profit is 9 and 0

Explanation:

Given

`x^2 - 4x = 5x`

Required

Determine the possible values of x

`x^2 - 4x = 5x`

Subtract 5x from both sides

`x^2 - 4x - 5x = 5x - 5x`

`x^2 - 9x = 0`

Factorize

`x(x - 9)= 0`

Split the equation

`x = 0` or
`x - 9 = 0`

`x = 0` or
`x = 9`

Hence, the number of cars that brings the same profit is 9 and 0