Would you care to (do something)?

This is a really polite, formal way to invite someone to do something. You use it like this:

Would you care to accompany me?

You can also ask with "for":

Would you care for a drink?

It's so polite that sometimes people use it with their friends as a joke. The joke is that you're speaking in a really formal way, even though it's not necessary.

This phrase appears in these lessons: