You might get close, but not for kids. Kids need milk, and milk is pretty expensive if you don't have cows (which take either extensive land or extensive feed.) Plus, teenagers eat a ton, it would be hard to properly feed a teenager for $10 a week at American prices unless you can grow (and preserve) a lot of your own food. Places where people live much more cheaply tend to have cheap local products (usually cereals) that form the bulk of their diets.
I was raised with little meat, maybe hamburger steak or chicken (extra roosters or hens that no longer lay) once a week and a ham or a turkey on holidays. Protein came mostly from eggs and beans; we ate pinto beans, cornbread, and fried potatoes at least two or three times a week, with raw milk and tea, and garden vegetables and greens. Go back a generation and my mother ate those same things fourteen meals a week, with some extra things added for Saturday and Sunday. Go back a few more generations and breads might make up 75% of the diet. In fact, a lot of the world still lives at that standard, with bread or rice at every meal. I'd be willing to bet lots of poor people today feed their children similar to my diet growing up. I'd be comfortable with food stamp people living at that level, but I'd guess most of them don't live a whole lot better right now. Probably the ones we notice are the ones scamming the system, buying steaks and such.
Also, most welfare mothers are not particularly bright or motivated and probably don't have the management and food preparation skills needed to maximize their budgets and nutrition, nor any way to get those skills. Nor, probably, do they have any desire for them. Instead they probably cook the things their mothers cooked, plus the things their kids want. So yeah, it's a shame that 1 in 8 Americans are on food stamps, but other than improving the economy (and reducing the share of it that government consumes) I don't see much alternative. As our manufacturing gets shipped offshore and our illegal population swells, there are going to be way more people than jobs in any unskilled field, so our spread between skilled workers and the unskilled poor is going to continue growing. Probably subsidizing these poor people does less damage overall than using government to artificially flatten the wage scale.