Convince my mom to let me get an Xbox360?

Ok, so I have wanted the Xbox 360 Elite for quite some time now. My dad is on board (heck, he even wants to play it with me) but as soon as I asked my mom she just started laughing and said no. -_- I would be paying for it with my own money ( I have about half saved up already) I am 15, I get good grades in school ( As and Bs) an I'd share it with my sister. My mom won't let me have it because she thinks I will be wasting my money, because I would be on it way too long and kill me eyes, and because I already have the Wii (Which I don't even play because it has horrible graphics and sucky games.) Are there any ways to convince her to let me buy it?