Even your friend's calculation is wrong. To stay three weeks, call it twenty nights, at $50 per night (plus taxes, service fees, tips?) would cost $1000 for lodging for the two of you sharing a room or $500 each, not $375. To calculate $375 per person, the total would be $750, which buys only fifteen nights. Does your friend plan to spend every third night sleeping on a bus or worse? In major cities, I would find it hard to believe that you can rely on finding a safe and acceptable place to sleep for only $50 per night, although it could be more realistic in small towns and rural areas.

Don't forget that language and health issues become more serious concerns when you go off the beaten path. Sleeping in a hut exposes you to more diseases and you need to plan in advance if you will be far from acceptable medical care.