You may be correct that he
needs that much, but it definitely is not a slam dunk and is dependent on his choices. Even on trips where I stayed in motels fairly regularly I have never averaged anything even remotely close to $100 a day. On trips where I got frequent rooms and ate in diners a lot and generally felt like I was splurging quite a bit, I still have always averaged under $50 per day for food, drink, and lodging.
Also as I previously mentioned, it is especially easy to go cheaply on the TA where it is extremely easy to find free places to camp, where you are likely to be able to stay indoors for free fairly frequently. The maps list quite a few places to stay in churches or with hosts and I have generally met folks who offered hospitality now and then. Most of the way staying in town parks for free is not a problem. It seemed to only be iffy within a few hundred miles of the coasts.
Well, the OP is traveling alone and planning on hotels a couple of days a week and that implies eating most meals out.
Not sure why you say that implies eating most meals out. Breakfast is often free with a room. Lunch and snacks on the road can just as easily be from a grocery regardless of where you stayed. Dinner may be more likely to be at a restaurant the two days a week he is in a motel, but the other 5 days a week it is likely to be in camp. In much of the middle of the country, rooms can be had for under $40 a night if you choose carefully. I know that I would try to pick nights where the room was cheap to stay in motels.