This is only a paradox because the framing of the question misleads people , partly by mentioning potatoes, into thinking that they are discussing something that one might actually do in the way it is described. In reality if you did this with real physical objects the part where it says:
"You let them dehydrate until they're 98 percent water"
hides a process in which one of the operations would involve picking up the potatoes. At this point you would notice that they were much lighter than before.
So as stated it is a trick question, the kind of parlour game found in old books of puzzles.
Finally, it seems to be a common failure of education to allow people to go through their 'mathematical' training and leave them with the impression that 'percent' is some kind of dimension when in fact it is short hand for a ratio: y is x percent of z. If z is not specified then you don't know what y is regardless of how much effort you put into discussing x.
So I suspect that in real life there are not many occasions when the paradox appears surprising.
So as stated it is a trick question, the kind of parlour game found in old books of puzzles.
Finally, it seems to be a common failure of education to allow people to go through their 'mathematical' training and leave them with the impression that 'percent' is some kind of dimension when in fact it is short hand for a ratio: y is x percent of z. If z is not specified then you don't know what y is regardless of how much effort you put into discussing x.
So I suspect that in real life there are not many occasions when the paradox appears surprising.