A brick weighs a kilo plus half a brick

Question

A builder says: "A brick weighs one kilogram plus half a brick." How much does a brick weigh? The quick answer of 1.5 kg is wrong; explain why, and find the right answer both by algebra and by a balance-scale picture.

Accepted Answer

2 kilograms. The equation. Let a brick weigh b kilograms. "One kilogram plus half a brick" is 1 + b/2. So b = 1 + b/2, giving b/2 = 1, so b = 2. Check. Half a brick is 1 kg, and 1 kg plus half a brick is 2 kg, which is a whole brick. Consistent. Why 1.5 is wrong. That answer treats "half a brick" as half a kilogram, quietly assuming the brick weighs 1 kg, which it does not. The sentence defines the brick's weight in terms of itself, and self-referential statements need an equation, not a guess. A picture. Put a brick on one pan of a balance, and a 1 kg weight plus half a brick on the other; t…

A brick weighs a kilo plus half a brick

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