There's a lot of science behind sound proofing. While your theory appears solid, that's not quite how it works. The 2 items together will do better but, not my those numbers.
I was able to do pretty well in my studio. The sounds you're talking about were actually the easiest to control. These were the mid to high frequency sounds and they were actually controlled with the construction of the walls. In my case, each opposing wall was layered slightly differently because this also helped. On one wall I would do a layer of soundboard, a lathing strip (to create an air space) and then a layer of 5/8 drywall. On the opposite wall, it would be a double 5/8" drywall with the lathing strip between.
The foam you're referring to is for the purpose you reference but, not for the purposes of sound proofing. It's to control those frequencies that cause feedback on microphones. I have truck loads of Auralex foam in my studio and it works well to cut down on the natural reverb in a room. They also make it in decorative forms for those of you with theatre rooms that would like a little better audio quality.
One last item but, I don't thing this is really an issue for BW. Low frequencies are not touched by the foam! The only thing that deadened that was the way the walls were layered in my studio. My studio was ~15' from my house. My wife would tell me if she turned the TV off and make the house quiet, she could hear the kick drum and sometimes the bass guitar but, that was it.
Sorry for being long winded.. Probably more info than anyone really wanted...lol