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A retailer sets the list price of a jacket by marking up its cost by 40 percent. The jacket is then sold at 10 percent off the list price, and the retailer still earns a profit of $78 on it. What was the jacket's cost?
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Correct answer
C
List price = 1.40 × cost. Selling price = 0.90 × list = 0.90 × 1.40 × cost = 1.26 × cost. Profit = selling price − cost = 1.26C − C = 0.26C = $78, so cost = $78 / 0.26 = $300. Check: list = $420, sale = $378, profit = $78.
The named false summit is (B) $260: a 40 percent markup followed by a 10 percent discount does NOT net to 30 percent profit, because the discount is taken on the larger marked-up price. The true margin is 1.4 × 0.9 − 1 = 0.26, not 0.40 − 0.10 = 0.30. (A) drops the discount; (E) mistakes the discount rate for the margin.
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