If you do want to go ahead and try to convince your mum, remember that there will also be electricity costs. my boyfriend was 19 and myself 18 when we got our girl, and one way we convinced his mum to let us have a snake was by paying extra electricity bills. The rules are we have to keep the snake in our room at all times, and we also own our own mini freezer. We pay for all of her food, care, vet bills etc. Vet bills are a big point as well; I don't know your financial situation, but will you be able to shell out possibly hundreds of dollars if your snake needs sudden care? Or will that fall on your mother?
Personally, I think that the best way for you to go about this is to borrow book/do research to help convince your mother that not all snakes are bad. For my boyfriend's mother, this took us about a year. The first time we asked she straight up said no, and so we did our research and presented it to her. Over time she gave in.
Best of luck to you!
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