OK, trying to remember all the way back to High School.......
Nope, my memory doesn't go back that far.
From a female perspective:
Both girls are quite pretty so I must say you have good taste. This is a bit of strange advice, but ask the girl that is most likely to say "no" first. Get that first no out of the way. As to figuring out which one that is, Ask your self the following questions:
Who does she hang out with?
Are there any guys in the group?
If there are guys, are there any ones that seem to hover around her?
Odds are if there is a guy already hanging around, then she may already have a date or a boyfriend.
Be casual, ask if she's going to the prom, if yes then if she's already got a date. If not then ask her if she'd like to go with you. Do act slightly dissappointed if she says no. If at all possible continue the conversation onto other topics. That will set up the possibility of a date at another time even if Prom is out.