USAMO 1980 Problem 1
- Day 1
- Answer
A balance has unequal arms and pans of unequal weight. It is used to weigh two objects of unequal weight. The first object balances against a weight A, when placed in the left pan and against a weight a, when placed in the right pan. The corresponding weights for the second object are and . A third object balances against a weight C, when placed in the left pan. What is its true weight?
Dataset text NuminaMath olympiads. Quoted with source.
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\sqrt{\frac{a-b}{A-B}} C + \frac{bA - aB}{A-B} \left( \frac{1}{\sqrt{\frac{a-b}{A-B}}} + 1 \right)
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