Chapter P, Problem 32PS

In mathematics, is is important to read the directions before attempting to work any problems. You are NOT expected to able to work any problems. You are NOT expected to be able to work Problems 11-60 at this time. You ARE expected to be able to work those problems AFTER reading this text. So for now, just place each assigned question in one of the following categories:

Yes. I know how to start this problem.

No. I don’t think I know how to start this problem.

Hopeful. If someone shows me how to proceed, I think I could answer this question.

Hopeless. I don’t think I’ll ever be able to answer this question.

A frugal man allows himself a glass of wine before dinner on every third day, an after-dinner chocolate every fifth day, and a steak dinner once a week. If it happens that he enjoys all three luxuries on March $31$, what will be the date of the next steak dinner that is preceded by wine and followed by an after-dinner chocolate?