Question

The quadratic function y = –10x2 + 160x – 430 models a store’s 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? Justify your choice.

Answer 1

Daily profit, y, as a function of T-shirts sold, x, is
y = -10x² + 160x - 430

In order to generate $50 in daily profits, the number of T-shirts sold is determined by solving the equation
-10x² + 160x - 430 = 50

Divide through by -10.
x² - 16x + 43 = -5
x² - 16x + 48 = 0

Answer:
This quadratic equation can be solved by factorization.

Explanation:
Note that
48 = 4 x 12, and
4 + 12 = 16
Therefore
x² - 16x + 48 = (x - 4 )(x - 12 ) = 0
The solutions are
x - 4 = 0  => x = 4, and
x - 12 = 0  => x = 12

Answer 2

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).