Which is correct?
Three patients are on a respirator
or
Three patients are on respirators
?
The trouble is they both sound wrong to me - the former sounds like they are sharing one respirator while the latter sounds like each of them is on multiple respirators - but one of them must be right.
This is an interesting question and I think the reason why both sentences sound correct and wrong at the same time is because conflicting rules of grammar are in play. I suspect both are correct although maybe the second sentence may be more correct. Let me explain.
If a patient on a respirator is thought of as being a complete unit (which is a perfectly reasonable way to view the situation) then the plural of "patient on a respirator" is patients on a respirator. However, if the patient and the respirator area thought of as being 2 separate units (which is also perfectly reasonable) then the plural is "patients on respirators".
Part of the difficulty is that most people are not familiar with respirators so they are not able to make assumptions that they would with other nouns. For example, if I said "3 patients have a donor heart", you would assume they all have one donated heart each and if I said "3 patients have donor hearts", you would still assume they all have one donated heart each because we already know that people would only need one heart.
By contrast, if I said "3 men are on a horse", you would think there are 3 men on a single horse but if I said "3 men are on horses" you would think they were each on their own individual horse, i.e. 3 horses in total, and not 3 horses each because we know you can't be on more than one horse at a time.
When people are more familiar with the item being discussed, the sentence is clear to them because their prior knowledge fills in the gaps.