I assumed the $3 referred just for food and not everything that goes with it. It was a pretty stupid and flawed assumption now that you've pointed it out.
As for your other question, I budgeted myself to $5 a day for food for a while and stuck to it without too much difficult.
It went like this:
Breakfast: Yoghurt and Muesli mix. I made my own yoghurt which makes it cheaper by a neglible amount but increases the fun.
A days worth of yoghurt comes out to a dollar or so, a $10 pack of muesli can last a couple of weeks.
Lunch: Sandwich or two ($0.35 bun, $0.20ish worth of meat, lots of peppers, spinach, tomato, red onion, cucumber)
That probably ends up being $1-$1.50
Dinner: Usually rice with lentils/beans or some sort of curry.
Rice and lentils are pretty much free. A months worth can be bought from loose change. The curry consists of whatever vegetables are on the discount rack plus spices.
Snacks: random stuff that was on sale that week. This is probably the most expensive part, especially if you snack all day. Stuff like dried fruit or bread with homemade dips is pretty cheap.
And that's a reasonably healthy, decent amount of food for $5.