If you're not eating organic, $100 for 3 weeks is easily doable for 1 person.
Here is what I eat on a workday:
8 oz fage yogurt
1/2 scoop of Brown Rice protein
1 hand full of nuts (walnut or pecan)
1 hand full of raisins
4 hard boiled eggs
1 banana, orange, or kiwi
8 oz coconut water
1 scoop of whey protein
3 hand fulls of "Power Greens" mixed salad from Costco
1/4 cup of grain (quinoa, farrow, or brown rice)
1/2 bag of broccoli from Trader Joes
I'm at about $7 a day and I'm eating healthy (and cutting).
If I just wanted to stay under the $5 mark I'd just buy whole chicken, eggs, cheap vegetables, and whatever grain was cheap.