Henry Ernest Dudeney/Modern Puzzles/186 - The False Scales/Solution

by : $186$

 * The False Scales
 * A pudding, when placed into one of the pans of a balance, appeared to weigh $4$ ounces more than $\tfrac 9 {11}$ of its true weight,
 * but when placed into the other pan it appeared to weigh $3$ pounds more than in the first pan.
 * What was its true weight?

Solution
Let $W$ ounces be the true weight of the pudding.

Note that we are discussing the weight of a pudding.

Hence the everyday avoirdupois scale is to be used.

First recall that there are $16$ ounces (avoirdupois) to the pound (avoirdupois).

Hence $3$ pounds more than in the first pan means $\tfrac 9 {11} W + 4 + 3 \times 16$, that is, $\tfrac 9 {11} W + 52$.

There are two different solutions to this puzzle, depending on how the false balance is faulty.