"Both the first and the last [plural]" vs. "both the first and the last [singular]" [duplicate]

There is a recorded announcement I hear several times a day on the trains I catch to and from work. Here is part of the announcement:

This train contains quiet carriages. Both the first and the last carriages are quiet carriages.

To me, this always sounds wrong. It feels like it should be

This train contains quiet carriages. Both the first and the last carriage are quiet carriages.

This feels more apt, since each of the carriages being mentioned are singular. You would say for instance

First and second place both get a medal

rather than places. Once you go to three or more things, then it is pluralised

The first three places get medals.

Is this all correct? It's been bugging me for a while.

Solution 1:

I believe that the announcement - while it could certainly be rephrased to be more pleasing - is grammatically correct. Try this: leave out "the first and the last", leaving "both carriages are quiet carriages". Adding "the first and the last" does not change the sense or the structure; it merely specifies which the carriages are meant by "both".

Your second example:

First and second place both get a medal

is not correct. If you wish to keep "both", then perhaps you could say

The runners in first and second place both get medals

otherwise, it should be

First and second place each get a medal.

Both implies a plural; each is singular.

Solution 2:

Both the first and the last carriage are quiet carriages can be seen in terms of ellipsis, that is, ‘the omission of elements which are recoverable from the linguistic context or the situation’ (‘Longman Student Grammar of Spoken and Written English’). Ellipsis normally occurs after the ellipted element has been mentioned. This would be the case in Both the first carriage and the last are quiet carriages. However, in the original sentence, the word carriage comes so hard on the heels of the first that it is the work of a moment to make the connection.

The same thing happens with the ellipted First and second place both get a medal. The expanded version would be First place and second place both get a medal.

The alternatives - Both the first and the last carriages are quiet carriages and First and second places both get a medal - are equally grammatical. Of course, it’s always possible to dodge the issue entirely with something like The first carriage is quiet, and so is the last and First place gets a medal, and so does second place.

Solution 3:

No, it's not all correct. Let's take them one by one:

This train contains quiet carriages. Both the first and the last carriage are quiet carriages.

Carriage should be carriages:

"Both the first and the last are quiet carriages".

or

Both the first and the last carriages are quiet. Not *Both the first and the last carriage are quiet.

First and second place both get a medal isn't how I'd put it, but I wouldn't argue with it. It's an elided sentence: the missing word is "holders" (placeholders).

It's perfectly reasonable to say "First, second, and third place all get a medal". Changing the sentence to The first three places get medals changes the structure of the sentence. And medals is incorrect because each placeholder gets one medal only, not multiple medals. However, most readers/listeners will know the meaning because they usually have sufficient background knowledge to understand that.

"Once you go to three or more things, then it is pluralised" is strictly your own ad hoc rule. Or can you cite a reference that specifies this as a rule? Some style manual or other? I doubt it.