subject and pronoun agreement?

[bosunyum]

It is very confusing for me whether to use plural or singular in the following examples.

ex) They lived happily for the rest of their life/lives(?)
ex)They could not solve their own problem/problems(?)

My questions is: when the subject or possesive are plural, the following noun should be plural?

[mykwyner]

You can use either one, depending on the point you want to make.

If the plural subjects share an object, then the object is singular.

They solved their problem. (They shared a single problem)

They solved their problems. (They each had their own problem or problems)

I'm not sure that I'd ever say that two people shared one life.