Sarbar is correct for eating out at restaurants, though the prices can be less in rural areas and the South.

If you are talking about shopping in grocery stores and preparing your own food, you can save a lot of money (just like home.)

For backpacking (hiking on a trail, not city-to-city in hostels), I can eat pretty well from a grocery store on about $10 per person per day. Less if I don't mind eating the same thing every day.

For car-camping, where I have more cookware, larger stove, and can spend more time preparing meals, I can cut that by a few dollars per person per day.

If you are talking about "backpacking" in the European traveler sense, then you'll probably be eating more in restaurants, but you can still go to a grocery store on occasion and save some money.

Does this help?
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--Ken B