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Phrase(s): care to do something
to want to do something; to be willing to do something. • I really don’t care to see that movie. • Would you care to go out for dinner?, Phrase(s): (Would you) care to...?
a polite phrase introducing an inquiry as to whether someone wishes to do something. • John: Would you care to step out for some air? Jane: Oh, I’d love it. • Sue: Care to go for a swim? Mary: Not now, thanks.
McGrawhill's American Idioms And Phrasal Verbs