Final answer:
To earn a daily profit of $150 from the sale of soccer balls, the store should charge a price of $20 for each ball.
Step-by-step explanation:
To find the price the store should charge for each soccer ball in order to earn a daily profit of $150, we need to set the given profit equation equal to the desired profit. The given profit equation is Y = -6x² + 100x - 180x, where Y represents the selling price of each soccer ball. So, the equation becomes -6x² + 100x - 180x = 150. Simplifying this equation, we get -6x² - 80x + 150 = 0. To solve this quadratic equation, we can either factor it or use the quadratic formula. Since factoring may not be easy in this case, let's use the quadratic formula.
The quadratic formula is x = (-b ± √(b²-4ac))/(2a), where a, b, and c are the coefficients of the quadratic equation. In our equation, a = -6, b = -80, and c = 150. Substituting these values into the quadratic formula, we get x = (-(-80) ± √((-80)² - 4(-6)(150)))/(2(-6)). Simplifying this further, we have x = (80 ± √(6400 + 3600))/(-12). Continuing to simplify, we get x = (80 ± √10000)/(-12), x = (80 ± 100)/(-12), and x = (20/3) or x = -30/2. However, since the price of soccer balls cannot be negative, we discard the value x = -30/2. Therefore, the store should charge a price of $20 for each soccer ball in order to earn a daily profit of $150.