Can you live on 15.00 groceries a week?

Yes, you can do so. I don't know how! You can't even buy enough cereal and milk for 3 meals a day for that amount. And a balanced diet would be very difficult. School lunches would cost half that a week. A box of cereal is going to go for about $4 and a gallon of milk on sale would be $2.

You could stave off starvation by buying cheap rice and maybe dented cans of vegetables. Meat would be maybe a can of tuna a week.