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If you wanted to study dance, why did you go to a school without - not that it matters.
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Marketing is a fluff major in the business school world and with few exceptions, will the where matter.
If studying dance is that important to you and you’re willing to start over socially and maybe lose some credits, then yes you should transfer - and the state school would be great!!
Prestige is overrated and frankly, who cares - because you can’t study what you want at the prestigious school.
It doesn’t seem complicated to me at all. Now should you choose the close to home public or another - might be a different question but the general question of transfer seems a no brainer - and if they have both majors you want, it’d be a fine school. Get an internship - and you’ll be fine. Frankly, to work in marketing, you don’t even need a marketing degree.
Good luck.