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.

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2016-04-09 08:52:03

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

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