Dating a rich girl?

Let me tell you some background.

There's this girl in college who suddenly is talking a lot to me, we met because we're taking one class together and the professor picked us to be on the same team for a homework.

She's invited me to drink coffee, the conversation flows perfectly, and we even agreed to do the final work of another subject together (we take the same course, with the same professor but on different days), yesterday I was the entire afternoon with her, we ate lunch together, watched a movie and progressed in the final work.

She's beautiful, we have some common interests and she's treated me better than any girl. The thing is, she's rich and I'm not, and this difference in social classes may become a problem over time

Should I try to leave things just as friends or what?
Dating a rich girl?
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