Question

The quadratic function y=-10xsquared+160x-430 models a stores daily profit (y) for selling a T-shirt priced at x dollars. What equation do you need to solve to find the selling price or prices that would generate $50 in daily profit? What method would you use to solve the equation?

Answer 1

Answer: The selling price of T-shirt should be either $4 or $12.

Explanation:

The given equation is $y=-10x^2+160x-430$, where y is the stores daily profit and x is the price of T- shirt in dollars.

The given profit is $50.

$50=-10x^2+160x-430$

$10x^2-160x+480=0$

$10(x^2-16x+48)=0$

Use factoring method to solve the equation.

$x^2-12x-4x+48=0$

$x(x-12)-4(x-12)=0$

$(x-4)(x-12)=0$

Equate both factors equal to 0.

$x=4,12$

Therefore, the value of x is 4 and 12, so the selling price of T-shirt should be either $4 or $12 to earn the profit of $50.

Answer 2

Answer:

Replace y in the equation with 50: (50 = -10x2 +160x - 430) Use factoring to solve the equation. After writing the equation in standard form and dividing each side by -10, it is easy to factor as 0 = (x - 4)(x - 12).