A vessel is filled with liquid, 3 parts of which are water and 5 parts syrup. How much of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup?

If we want to have half of water and half of syrup we should have the same amount of those two components.

Firs we have 3 parts of water 5 parts of syrup

If we draw off 1 part of syrup and replaced it with one part of water we will have

water: 3+1=4

syrup:5-1=4

So 1 part of syrup must be drawn off