For the berry version:
I boiled about 1 frozen cup berries in a minimal amount of water until warmed and mushy, drained and pureed to make around 1/4 cup of puree. If you have the time, thawing them to room temp would work fine too. Or heck, just puree them frozen if you don't mind slightly bigger chunks. You'd retain more nutrients that way. In the picture, I used blueberries and raspberries and took the extra step to separate out the little seeds using a sieve. (Cray cray, I know, but the girls and I can't stand the little seeds!)
1 cup frozen berries makes about 1/4 cup berry puree.
1/4 cup puree + 1 cup applesauce = berry applesauce!
If you wanna just make a whole batch of berry applesauce, then use 3 cups of frozen berries and puree!