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5 ingots of different weigths (II Soros Olympiad 1995-96 R3 9.9)

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June 4, 2024
algebra

Problem Statement

There are 55 ingots weighing 11, 22, 33, 44 and 55 kg with an unknown copper content that varies in different ingots. Each ingot must be divided into 55 parts and 55 new ingots of the same mass of 11, 22, 33, 44 and 55 kg must be made. This requires that the percentage of copper in all pieces be the same, regardless of what it was in the original pieces. What parts should each piece be divided into?