My girlfriends Escort Zx2, idk what year...anyways, we were on the east side last night and the car's interior lights started to dim and the battery light came on. The car soon sputtered and died. Tried to start it back up, and it doesn't crank over. Jumped it, and it started right up, just to die right away when it was taken off the jumper cables. I'm assuming its the battery took a shit, or the alternator did. Both the alternator and the battery look like they are pretty old. The girlfriend said at no other times before last night did the battery light come on.

Any advice or should I just take out the battery and alternator and have them both tested to see which is bad? Or just replace both since they are both old?