How do I convince my parents to let me dorm?

I did some quick math. If my car has 30mpg, it’s more than 20 miles drive, and gas is around $4. It would cost more than $6 to get there. Going there and back 5 days a week for 4 weeks means more than $240. That’s still much less than $1000 monthly rent. However, if I work, I think I can make $760 a month. Thing is, I’m also thinking of double majoring so time is gonna be problem.