I spend half that for 2.5 adults. (The .5 is for a Mongolian student who lives with us but doesn't always eat with us, but who does use food.)
Several suggestions:
1. Use cloth diapers rather than paper diapers - much, much, much cheaper in the long run.
2. Make your own babyfood from in season food.
3. Make your own bread from whole grains purchased in bulk.
4. DO NOT use processed, packaged, or convenience foods. Cook from scratch.
5. Use less expensive oatmeal, etc. for breakfast rather than expensive, nutritionally useless cold cereal.
6. Learn to cook from scratch with dried legumes.
7. Shop the case lot sales. If you buy case lots of what you use most on sale, that will save you money. Do not exhaust the case lots, though. Most stores have about a six week sale cycle. When the item comes on sale again, replace what you have used on sale. That way, you never have to buy the things you use most when they are not on sale and you always have some of that item on hand.
8. Shop in bulk for staples. Making bread from hard red wheat acquired from Costco or the Lindon Cannery results in better and more nutritious bread (per my home teacher) and much less expense than buying ready made bread or even bread made from staples purchased in smaller, more expensive packages.
9. Get a freezer and only purchase meats and other frozen items on sale.
10. In season, save on produce by growing your own in your garden. If you have excess, you can dehydrate or can it and use it in the winter to reduce your reliance on grocery store items.
Good luck and have fun.