Currency Density

Consider the following riddle:

You are robbing a bank and can only carry 100 pounds (45 kilograms) of currency out of the vault. Once inside, you see that the bank has organized its money into large piles of Dimes, Quarters, and Half Dollars. How do you pack your bag, taking from these piles, so that you maximize the amount of money you get?

(answer is below)

The answer is that it does not matter how you pack your bag, as all three of the listed coins have the same "value density" (i.e: 100 pounds of dimes is worth exactly as much as 100 pounds of quarters and 100 pounds of half dollars).

Coin NameCoin Value in CentsCoin Weight in GramsDensity (cents/gram)
Quarter Dollar255.6704.409
Half Dollar5011.3404.409

Consult the United States Mint's currency specifications for proof.

By the way, the bag you take from the bank will have just shy of two grand.

100 (lb) * 453.59 (g/lb) * 4.409 (cents/g) * 0.01 (dollar/cent) = 1999.88 dollars