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Answer to old chestnut: water and wine:

There is the same amount of water in the wine as there is wine in the water.

To understand this, let X equal the volume of water in the wine and Y the volume of wine in the water. Since it is a closed system, we must have 1 gallon - Y wine in the wine and 1 gallon - X water in the water. However, the total volume in each container is still one gallon, since we removed a teaspoon and added a teaspoon to each container. So 1 gallon - Y + X = 1 gallon, so Y = X.

This type of analysis is at the heart of material and energy balances, the first distinctly chemical engineering course most chemical engineering students take. The calculation above is a material balance on one container, accounting for all the flows in and out of the container and the initial and final contents of the container.

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