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Tags: AMC, USA(J)MO, USAMO, algebra unsolved, algebra



A two-pan balance is innacurate since its balance arms are of different lengths and its pans are of different weights. Three objects of different weights A, B, and C are each weighed separately. When placed on the left-hand pan, they are balanced by weights A1, B1, and C1, respectively. When A and B are placed on the right-hand pan, they are balanced by A2 and B2, respectively. Determine the true weight of C in terms of A1,B1,C1,A2, and B2.