Duke University has a $6.0 billion endowment as of 2013, subsidized by the US taxpayer through favorable tax treatment.
And because of that endowment, almost no Duke students actually pay the rack-rate of $60K per year.
Private universities and colleges with fat endowments only charge rack-rate tuition to folks from well-heeled families who barely made the admissions cut. Everyone else gets scholarships in amounts based on how much the university wants the person to come. We paid the equivalent of in-state tuition at a state school to send our daughter to a private liberal arts college on the East Coast with a rack-rate tuition of $45K/year: she was from Kansas (geographic diversity!) and entered with enough college credits that she’d have walked in the door of a state university as a second-semester sophomore (with calc, freshman comp, and her whole language requirement for a B.A. out of the way) — they jolly well wanted her to come, and gave her big scholarships plus work-study jobs.