That's about $8/day. I probably spend close to 10x that on food living in Manhattan. Granted I go out a lot and that's including drinks at dinner, but even not going out to eat at all and fasting every other day I have no idea how I'd only spend that much.
I can see it if you go out a lot, but for groceries it's fairly hard for me to spend more than $200/mo. I don't have a car, so just physically carrying $500/mo of groceries to my apartment would be quite an effort! I can't imagine how I'd do that unless I bought mainly stuff with a really high price:weight ratio, like steak or something, which I do occasionally, but don't eat as a staple food.
Today, for example, I carried what seemed like an uncomfortably heavy set of bags, yet it only came out to about $30, and will probably last me the rest of the week: 2 lbs pork tenderloin (2x $5), 5 lbs potatoes ($3), 2 lbs tomatoes ($4), 1 lb lentils ($3), 2 lbs onions ($2), 1 head broccoli ($1), 12x eggs ($3), 2 lbs nectarines ($3).
I think I more often run into the problem of buying way more than I can carry/eat, and it still doesn't cost much. I mean, I like nectarines, but 2 pounds of nectarines is a lot to finish before they get overripe, so some of that might get wasted. But since they cost me damn near nothing, that's alright.
Cook them! Throw them in a pot with some brown sugar and spices. Or throw it in a crockpot/baking dish with {1/2 c. butter, 3/4 c. flour, 3/4 c. (brown) sugar} sprinkled on top, bake, and shazzam! Cobbler!
I feel comfortable, looking at average household food costs, in saying you're an outlier if it's "fairly hard" to spend more than $6.67 a day in the United States (let alone Manhattan) on groceries.
While the way we eat is certainly an outlier (and I know it), I'm equally as sure that you are too.