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A and B go to the same wholesale market every time to buy white sugar. A's purchasing strategy is to buy 1000 yuan of sugar each time; B's purchasing strategy is to buy 1000 Jin of sugar each time. Recently, they both went to buy sugar with different prices twice. Who's the average price lower?
Suppose that the price of buying sugar twice is x and Y (unit: yuan / Jin), and a and B are the average price of buying sugar for a and B respectively, then according to the meaning of the question: a = 2 × 1000x + 1000y = 2xyx + y, B = 1000x + 1000y2 × 1000 = x + Y2, ∵ B-A = x + y2-2xyx + y = (x + y) 2-2xy2 (x + y) = x2 + Y22 (x + y) > 0, ∵ A's average price is lower, then a's method is more cost-effective
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