Your figure matches about what it costs to go to a private school, but, from my experience, public schools are also more likely to give scholarships [2]. Even still, no one is forced to go to a private school.
[1]: http://www.collegeboard.com/student/pay/add-it-up/4494.html
[2]: I went to a private school my first year. It was around $30k/yr, but I was also given a scholarship that cut that price to around $18k/yr. Most of the people I met on campus also received scholarships of some sort as well.