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

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).

Answer 2

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

Step-by-step 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.