1980 USAMO Problems/Problem 1
The effect of the unequal arms and pans is that if an object of weight in the left pan balances an object of weight in the right pan, then for some constants and . Thus if the first object has true weight x, then .
Similarly, . Subtracting gives and so
The true weight of the third object is thus:
Credit: John Scholes https://prase.cz/kalva/usa/usoln/usol801.html