It is always going to be a guess in some ways. One option is to write out a typical menu and then cost that out for a total, divide by the number of people served and that will give you the average per person and then multiply that by the total number of meals served.
Another option is to add up all of the grocery bills and divide by the number of people that served and then multiply by the number of kids served.
In a pinch when I was running behind the times I took 2 months worth of grocery bills and just used those with the formula. Once I did meals all the ways to see which one was to my advantage and there was less than a $150 difference from one method to the other which is not a lot of money in the grand scheme of things since it will never be a precise science.
To do the cost per day method doing the menu will be your best. Make up a 3-6 week menue based on what you normally served and then cost it out. You probably do more repetition that you think in the sense of every Monday could be hamburg with something so one week with noodles and spagetti sauce, week two with box of hamburg helper, week three as meatloaf, etc. After you have done it a couple years you will figure out which method is the easiest for you.
If you use excell you can easily input the amount on the grocery receipts and add the formula totals the columns for you. The daily amount will vary for each person based on what they serve and that is why you can't use the arbitrary per day amount. The $7 is that red flag type of number in the sense that if you are claiming expenses a lot above that they will question you but you can claim pretty much anything below that and be ok it's just that you have be able to show them how you arrived at the number you are using should you be audited. That is the total key - no audit and any method works - get audited and you run the risk of being denied claims.