Valid question. I went back and added up the numbers provided, replacing the 12-month studio lease presented with basic housing then subtracting the summer expenses - but I don’t know how I found 38-40… I found tuition 33k, total with basic room&board 43k though housing varies from 6,400 to 10,100 a year; Blount&Honors would be 8,400 and Lakeview 9,200, and there are 2 meal plans (though the big one with 3 all you can eat meals a day + snacks seems really too much and the $1,000 savings if you take the silver Plan can go toward a LOT of food if OP is a growing boy who needs lots of food all day long. IMHO, the “Silver Plan” sounds perfectly adequate as long as OP eats a cereal bar or instant porridge for breakfast, “cooks” once or twice a week, and/or orders pizza once. Basically what most kids do AFAIK.)
In the end, regardless of how we add things up, OP with a 15k scholarship is within budget and even more so if he gets a 1360+SAT score for the 24k scholarship (which seems achievable from a 1330). His uncle is being very generous with the 35k and that goes a long way.