I know this sound crazy but I was thinking 200 dollars it gives him 50 dollars a week for food and that is what DH and I spend a person.
yes, it might seem reasonable, but does your son have the knowledge and skills and foresight to plan meals ahead the way you do and cook them efficiently? Does he have access to all the necessary kitchen equipment in the apartment where he will be? How much freezer/fridge space will he have?
When my DH shared an apartment with 3 other guys, the fridge/freezer space was always an issue. Each of them prepared their own meals and did their own shopping. That mean there were 4 gallons of milk, 4 bottles of juice, 4 bottles of ketchup, etc in the fridge. Each bought their own bag of frozen fries, etc. So the freezer space didn't always work so well. That made it hard for my Dh to plan meals ahead, cook and freeze things, etc becaue there just wasn't room to do it efficiently. That might contribute to him needing to shop more frequently, not buy in bulk, not be able to save leftovers, etc, all of which will cause him to have to shop more frequently or buy things at a higher price (ie whatever price chicken is this week, he pays because he can't buy several weeks worth at the sale price).
And he might not have an easy time getting to a good grocery store. At homme, you might shop several stores to get various sale items. A male college student isn't going to have the time or conveience of doing that.
I think you need to figure closer to $100 a week, and should consider putting SOME money on a dining account at the school, there are going to be a lot of times that he is jammed up with work and not going to have the time or energy to cook.