Yes, that is true, the STUDENT pays more... but the college receives the same amount. Being public, they receive public funding based on the number o students from that state/country based on the state/federal funding level.
Here in NY, take off about 10k-12k for the instate price you have and you get the SUNY (State University of New York) price. Binghamton is about $18k with room and board, but I have the smallest meal plan available.
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