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Potatoes with different fillings - baked, mashed, boiled…
Lentils - as the basis for salads and curries.
Cauliflower rice - a little cauliflower goes a long way.
Soups - different veg and whatever bits of meat or chicken you can afford - potato, leek and bacon is a cheap and tasty soup.
Also, you don't have to eat the same as her. For example, make a nice pumpkin and chick pea curry and cook some rice. A little cauliflower rice in the microwave for her, both of you have 'curry' over rice and you can take the leftover rice to work for lunch.
Buy a loaf of cheap wheat bread and freeze it - take a out a couple of slices for your lunch and it will thaw for work, but leave the more expensive wheat-free bread or corn thins for your sister.
There are some organisations that do a huge box of groceries for $30-40. Depending on your location. If you can't get anything then slow cooker is a great idea. I made enough for 3 nights for about $15 for my husband, myself and the kids.
You can grate a cauliflower and keep it in the fridge for about a week. You can use it to replace rice. I use it with curries,make paella, or whatever else you can think of.
Uh... why can't she pay more? I mean, I get that you're sharing, but as sisters, does a few extra dollars matter? I've never shared with family, but with friends etc and we just did our own food. I found stir fry to be a good, economical meal, no need for rice etc. Aldi is good for staples, particularly cleaning products and toiletries.
What are the dietary issues she has? If we knew, we may be able to offer suggestions for alternatives
Broccoli, Carrots and Potato (generally the cheap veggies) Grilled chicken (pack of 1kg chicken breasts is cheap and she can change it up by using different spices on it), you can usually get single pork chops for $3-4 or pieces of steak for less than $10, Eggs and Bacon, Salads, Tin Tuna, Ham?
My youngest daughter is a celiac and we've cut out all gluten and wheat at home. There are alternative products now but some can be expensive, but Woolworths has their own select range of gluten and wheat free cereals for a decent price. She can get veggie and coconut chips for snacks as well.
$60 is quiet a decent amount to feed one person a week. I feed all 6 of us on $170 max a week and that includes breakfasts, lunch and dinners for the week. Just have to be creative.
Cous cous (can she have that)? Oats, polenta, potatoes, eggs, go fishing, nuts, grains, cheap vegetables, if nothing else go see St Vincent de Paul and tell them your predicament, they may be able to help you out with a basics card.
If you can, join a co-op or find a bulk buy store. Work out what works for you both (I'm not gf but friends are and use almond meal a lot so buy it in 10kg bags) and meal plan!!! Meal plan is so important to minimise waste. You can make crackers from seeds and chia etc. start googling recipes.
Oats, cheap and filling.