why an xbox elite? A playstion 3 is better. an not because im obsessed with sony like losers out there but because its logical (if thats a word) especially now that the ps3 slim has come out.
it only cost 300 and it comes with 120 gb which is the same thing as the xbox elite which is 300 with 120 gb also. and the internet is free unlike the 360 which you have to pay to play online. and the ps3 has an internet browser so its also like your using a comp. and you can also gameshare with people who have a ps3, like if the buy games through the download catalog they can share it with you too, thats getting free games right there. and the xbox 360 has a high chance of getting the red ring of death. but to the microsoft fans out there dont take offense cause i dont mean it, but its smart, and they say the online is better then the ps3, DONT BELIEVE IT, its both the same thing,you play online with other people while talking. same thing! But then again its your choice. let me stop talking so much and just answer your question, do good in school if you dont already, or bribe her, like tell her you'll do this and that , etc if she gets you the xbox, and like talk about it. like say the good things about it. etc. if that doesnt work then just look all depressed, and just tell her honestly your bored and you would like something new. if that doesnt work. if you have valuable stuff sell it and if its still not enough show her you have half of the money so she can put in the rest, be like "mom i got half of the money atleast you dont have to put all of it in.( thats also a good idea cause if she grounds you she cant take away the xbox cause you can tell her i put half of the money in too.") or you can ask her to buy you a used one if you dont mind. and if none of that works, just nagg her until she cant take it no more. so you can show her you really want it.
This is all i can say, good luck my friend!

a new gamer is always welcomed in to the community!
