Bank robbery word problem

Question

A bank was robbed and a lone robber carried the loot away in a bag. The money stolen may have consisted of $50 and $100 bills, or only $100 bills, or a combination of bills ($5,$10,$20,$50,$100).

How would I be able to figure out whether or not a person could carry any amount of money using any combination of dollar bills. Is there a general method or formula to prepare for future bank robberies?

Thank you.

Answer 1

All denominations of US paper bills are equal in weight and size, so 100 $1 bills have the same weight and volume as 100 $100 bills ($10,000).
1,000 bills weigh about 1kg, approx 2.2lbs. If an average man weighs 75kg (165lb) and can comfortably carry and run with a small briefcase or suitcase weighing up to 5kg when empty containing the notes up to 10% of his weight (7.5kg) then his loot will be limited to 2.5kg (5.5lb), which is 2,500 notes.
2,500 $100 bills=$250,000.
So he (or she) could carry any amount between $2,500 and $250,000.
What about bulk or volume? The surface area of a note is about 15.6cm*6.63cm=103sq cm.
If notes are bundled to a thickness of 2.54cm (1 inch) the volume of the bundle=263cc or 263ml. Call this 250ml=0.25 litres.
A small case 30cm*60cm*10cm has a capacity of 18,000cc or 18 litres, which will hold about 72 bundles.
If a bundle contains 200 notes, then the case will hold about 14,400 notes and weigh about 14.4kg (nearly 32lb!), about $1.44m in $100 bills.