To backpack around some countries in Europe for a month? Figures in American dollars would be preferred.

I'd like to hit up Belgium, France, Amsterdam, Scotland, England, and Germany. Would it be around $10,000 U.S.?

Unless you plan on doing some heavy spending... $10,000 dollars is a bit excessive. Unless you were to maybe travel the whole continent + North Africa/Mediterranean Middle East.

Could you get by on less than $100 a day?

If you plan on living large...about 60 dollars would do...if you don't mind living in hostels and scrounging for food, you can get by with 30 dollars a day...