Find the weight
A pudding, when put into one of the pans of these scales, appeared to weigh four ounces more than nine elevenths of its true weight, but when put into the other pan it appeared to weigh three pounds more than in the first pan. What was its true weight?
If the scales had been false on account of the pans being unequally weighted, then the true weight of the pudding would be 154 oz., and it would have weighed 130 oz. in one pan and 178 oz. the other. Half the sum of the apparent weights (the arithmetic mean) equals 154. But the illustration showed that the pans weighed evenly and that the error was in the unequal lengths of the arms of the balance. Therefore, the apparent weights were 121 oz. and 169 oz., and the real weight 143 oz. Multiply the apparent weights together and we get the square of 143-the geometric mean. The lengths of the arms were in the ratio II to 13. 154 and 143 is the true weight
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