I had a really bad Physics 1 Prof in college but I remember this formula:
C1V1 = C2V2
It's quite useful in brewing. C = Concentration and V = Volume. The 1s and 2s are supposed to be subscripted. You can use any units you want as long as they're the same on both sides of the equation. This won't account for your newly added alcohol that the 1 gallon of applejuice would add though. Sounds like drunkatuw got that one for you.
EDIT: Woops, Yooper said the new applejuice isn't being fermented
, so you can use that formula to get the same answer you got in your OP.