Ooo! I missed this. Is it $50/week, or for the whole month?"50 Dollar February" will be for the whole month of February!
I've read about these kinds of challenges before. It's part of what inspired me to try to limit my grocery store spending to $100/week. For just DH and me, that should be plenty. It's also $100 at THAT store. I get a lot more than food there, so it includes socks, soap, headlights, wiper blades, shampoo, etc. It does not include prescriptions or dog food.
This is my third year, and if you say $5200/year, I think I'll be under by about $400 for the third time. There are some weeks I'm under, but a few I've gone over.