I took the data provided by enth above, added some figures found in my own research, and tried to estimate the ratio of face value to market value of this particular distribution of loose change.
All American coins currently being produced for general circulation contain two of three metals in various proportions: copper, nickel, and zinc.
The penny or one cent coin weighs 2.5 grams and is 97.5% zinc, 2.5% copper by weight. A zinc core is coated with copper, which is why the coin has a copper color. Using enth's data, I calculated the metal in one of these coins to have a market value of 0.035¢. Prior to 1982, pennies were made from 95% copper. An older penny is worth about 0.435¢ as scrap metal, but they're still in circulation since their intrinsic value hasn't yet exceeded their face value.
The five cent coin is commonly called a nickel despite its composition of 75% copper, 25% nickel. Weighing in at five grams, the nickel contains 1.43¢ worth of metal.
The ten, twenty-five, and fifty cent coins, called the dime, quarter and half dollar respectively, are identically composed of 91.67% copper and 8.33% nickel. A mostly copper core is sandwiched between two layers of nickel in these coins, which were made of 90% silver until 1965 (those aren't in circulation any longer). Their masses are 2.228, 5.67, and 11.34 grams, the ratio of which is identical to the ratio of their face values. The metal in these coins is valued at 0.479¢, 1.20¢, and 2.40¢.
There are also a few varieties of dollar coins, but one is unlikely to appear in a lot of loose change, so is not included here.
I analyzed several possibilities for a group of coins weighing slightly over 11 pounds (5 kilograms after my conversions, to make calculations easier) and having a face value of about $117, and came up with the following plausible scenario:
- 700 pennies, $7.00 face value, 1.75 kilograms. I estimated a 4:1 ratio of zinc to copper coins and arrived at a market value of about $0.80.
- 200 nickels, $10.00 face value, $2.86 market value, 1 kilogram.
- $100 face value of any particular assortment of dimes, quarters, and halves, all of which have the same face to market ratio. Halves are uncommon, so the actual box might have contained 300 quarters ($75.00) and 250 dimes ($25.00). The market value of these coins, weighing about 2.26 kilos, would be about $4.80.
The metal in that $116.97 box of change was worth about $8.46. Loose change, at least in the U.S., seems to be worth more than thirteen times the value of the metal it contains. Not that this really matters until the government collapses, though - paper money isn't worth anything without the declarations of the Federal Reserve to back it.