Question

A company sells widgets. The amount of profit, y, made by the company, is related to the selling price of each widget, x, by the given equation. Using this equation, find out how much the widgets would have to be sold for, to the nearest cent, in order for the company to break even. Only enter one possible price. y=-x^2+77x-615 y=−x 2 +77x−615

Answer 1

Answer: the widget would be sold for $84.3

Step-by-step explanation:

The amount of profit, y made by the company, is related to the selling price of each widget, x, by the given equation which is expressed as

y = - x² + 77x - 615

At the point of breaking even, profit = 0. This means that

- x² + 77x - 615 = 0

The general formula for solving quadratic equations is expressed as

x = [- b ± √(b² - 4ac)]/2a

From the equation given,

a = - 1

b = 77

c = - 615

Therefore,

x = [- 77 ± √(77² - 4 × - 1 × - 615)]/2 × + 1

x = [- 77 ± √(8389)]/- 2

x = (- 77 + 91.59)/2 or x = (- 77 - 91.59)/- 2

x = - 7.295 or x = 84.3

Since the price cannot be negative, then x = $84.3