So your mum won't just you know, give you the money and let you make the decisions and experience the benefits (or in her mind, consequences) of building a PC? STICK IT TO HER. TELL HER YOU'RE AN ADULT, YOU CAN MAKE YOUR OWN CHOICES.
But for the record, when I was buying my prebuilt, I was told that it was a really good deal and that there was no way I'd be able to build the same thing for a lower price. Though that might've been a one in a million thing.