Brain is singular and Brains is plural.
If I talk about one person's brain , I use singular and for more than person's brain I use the plural,righ?
For example,
1.Use your brain.
2.He killed people and ate their brains.
So, in these two cases, we mean the organ inside our skull and the organs can be counted- so we should use singular/plural numbers.
But when we say "Beauty with Brains", obviously we do not mean a lady with more than one of that organ , we mean "intelligence" by "brain" here,right, and "intelligence" cannot be counted.
Now, here is the problem that encountered: "We need to put our brain to work to make sure it stays fit for long."
Should not this be brains and not brain? Because we are talking about our brain that is the brains of more than one people, i.e., more than one of that organ,so should be in plural number. And even if we are trying to mean 'intelligence' then also we should use the word 'brains' no? So, either way it should have been 'brains'. "Brain" is wrong.
Best Answer
Your assertions in the first part of your question are correct - we use the word 'brain' both to describe the organ inside our heads, and as a synonym for intelligence. So to quote your examples:
Both refer to the physical organ, in singular and plural form, respectively.
In this case, 'brains' is a synonym for intelligence, so again you are correct.
Ignoring the oddly worded ending to the sentence, I would argue that the sentence is not gramatically correct. In the first half of the sentence, the personal pronoun 'we' and possessive determiner 'our' imply that we are talking about more than one person, but in the second half of the sentence only one brain is being referred to, as evidenced by the singular 'it', in 'to make sure it stays fit for long.' So it would probably be best to pick a side...
Either
or
would be good starting points.