Puzzling Handshake

A fun puzzle: [hint- try making a chart - this is geared for 5th graders so it's fun not hard.]

A group of people met at a party. Each person shook hands with everyone else only once. Mr. Li shook hands with 3 times as many men as women. Mrs. Li shook hands with 4 times as many men as women. How many men and women were there at the party?

I hate shaking hands. Especially because it is such a socially masculine thing. If a woman shakes strong, people think she envies men or wants to overpower men or some such nonsense. But if she shakes weak, people think -typical girlie-girl- the poor thing barely has the strength to grip. So no matter what, you are regenerating a stereotype everytime a woman shakes hands. What's a girl to do?