## Faulty Scales

#### Problem

A boy stands on a set of faulty scales that record his weight as 52 kg. His sister's weight is recorded as 56 kg and their combined weight is recorded as 111 kg.

What is the true weight of the girl?

#### Solution

To solve this problem, we shall assume that the scales add or subtract a constant amount from the true weight.

The boy's weight, including the error, is recorded as 52 kg. When his sister steps on to the scales, the increase in weight, recorded by the scales, will be equal to her true weight. Hence, the girl weighs 111 52 = 59 kg, and we deduce that the scales subtracts 3 kg from the true weight.

How can we be certain that the scales, instead of adding/subtracting a fixed amount, don't increase/decrease the weight by a particular scaling factor?

Problem ID: 221 (24 May 2005) Difficulty: 1 Star