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I am in a similar situation to you, in that we are on a very limited budget for food buying. I know you didn't ask this, but I tell everyone I can about shopping at the cheaper stores such as Price Rite or Save-a-Lot, depending on where you live in the country, that are cheaper than the "chain" supermarkets. You can look at www.priceritesupermarkets.com or www.save-a-lot.com to see if there are any near you. If there are not any of these near you, do some research, there may be other stores similar to this near you. If you don't have these stores, always buy generic or look for sales or stuff you can buy with coupons. Also, many of the bigger stores often have a rack for discontinued or damaged items at half price, and also "Yesterday Bake/Produce" at half prices, or meat with coupons on it that say something like "Reduced for quick sale" and take a good amount off. Just make sure you use these right away, or freeze it.
At Price Rite, I buy stuff like 1 pound of ground turkey meat, which is just like hamburger meat when cooked, but healthier, for $1.49, and use it for two meals, instead of using 1 pound for each meal, even when a recipe calls for one pound, although with 6 kids, I don't know if you can split it in half. Stuff like hamburger helper at stores like this are cheaper (they even have their own brand for like .89, for when you do buy hamburger helper). I buy buillion cubes and try to make a lot of soups where I can combine many of the frozen vegetables I buy for dinners in the week and mix it with 1/2 pound of the turkey meat, beef buillion cubes, water, potatoes or rice and veggies (put whatever kind you like in there.) Or, if I've made a whole chicken (which you can get at these stores pretty cheaply), and I have leftover chicken that I cut off after we're done (try to get all the chicken off), then I use that leftover chicken for soup the next night with chicken buillion cubes, water, chicken, rice or noodles and whatever veggies you like. You can use canned instead of the frozen veggies in both of these soups, and I'm sure it would still be good. Of course, you can add regular white bread (.69 at Price Rite), buttered, to the meal to dip in the soup and it helps fill everyone up. As for the frozen veggies I'm referring to, they sell 1 pound bags of frozen veggies for like .89 to $1.19, and I can get several meals out of each bag.
You can buy potatoes, cut them up, put either melted butter, or oil on them and sprinkle them with spices such as garlic salt, onion powder, pepper, (really whatever you like), and bake them in a 375 degree oven for about 15 minutes, until tender. They can go with just about any "meat" meal to help fill everyone up.
I also make a dinner where I take pizza dough, spread it out on the pan, put on bologna, or salami, or both, (or any other type of pre-packaged lunch meat you have and/or like) with some cheese, roll it up, put butter and garlic salt on the top, and bake it in a 375 degree oven for about 20-25 minutes until golden brown on top, and not doughy inside anymore. Slice it up, and it feeds several people. The potatoes I described earlier go good with this meal.
Also, when I'm going to have certain types of dinners, like say tacos where I have to buy the soft fahita shells, cheddar cheese and salsa, I'll make similar meals that will make buying those items more cost efficient. For example, nachos (1/2 pound turkey meat, and salsa over nacho chips with cheese/olives/onions, etc. on top.) As for the tacos, you can add canned corn, tomatoes and beans (white, pinto, etc.) to the meat and it will bulk it up.
You can also make shephard's pie with 1/2 pound ground turkey meat, cooked, mixed with 1-2 cans of creamed corn. Put that in the bottom of a baking pan and spread mashed potatoes on top. I usually put american cheese on top, but you don't have to. Bake in a 375 degree oven for about 10-15 minutes. Make gravy for people to put on top, if they want it. (By the way, gravy and taco mixes are .29 to .39 at these stores.)
Pasta dishes are also a cheap option, mixing 1/2 pound of cooked ground turkey meat with tomato sauce (cheaper than pasta sauce in the jar) mixed with whatever spices you like, then mixed with spaghetti, elbows, ziti, or whatever pasta you like/have. And of course, the pasta can be left plain to be served with butter and garlic or garlic salt. Serve some frozen veggies and buttered bread on the side, and there's a meal.
Cheap hot dogs with a can or two of baked beans makes a good meal, added with mac & cheese and/or those potatoes I mentioned earlier.
Price Rite sells the boxes of Banquet Fried Chicken for $4 (with about 6-8 pieces of chicken in each.) Serve it with potatoes, rice or pasta and a veggie, and there's another meal.
I also make what I call "little pizza's". I take the buttermilk bisquits that come in the blue can in the refridgerated section. I cook up 1/2 pound of turkey meat (but you can do it without the meat) and mix it with tomatoe sauce that I make myself. Put a little bit of the meat/sauce mixture, or the sauce, on each one with a little bit of velveeta, mozzarella, or american cheese on top. Bake in a 375 degree oven for about 6-8 minutes (keep an eye on it so they don't burn.) Two cans of biscuits, which you can get pretty cheap, make 20 little pizza's, served with potatoes and a veggie. Yum!
One other idea of something to help you get more food is to go to food banks. You can start at your local Salvation Army, and while there ask if there's a list of the food banks in the area. You can go to a different food banks,just don't let them know you've gone to other ones. (Desperate times call for desperate measures.) Usually you'll get free bread/bakery items, and they also give out cheese and/or milk, canned fruits and veggies, cereals, sometimes soups, tuna, and rice and/or pasta and/or instant mashed potatoes. This all can help your food to go a bit further.
These are just some ideas of what I do, I hope this helps. Good luck!!