Question by solcruz: Another conversion question?
In 1933, the United States went off the international gold standard, and the price of gold increased from .00 to .00/troy oz. The twenty-dollar gold piece, known as the double eagle, weighed 33.436 g and was 90.0% gold by mass. (a) What was the value of the gold eagle before and after the price change? (b) How many coins could be made from 2.00in3 of gold (1 troy oz.=31.1 g; d of gold=19.3g/cm3)?
Best answer:
Answer by ltpowers
The value of the gold is its mass times the price.
We know the mass of the coin, but only 90% of it was gold:
mass of gold in the coin = (33.436g * 0.9) = 30.0924g
Now we also need to convert that into troy ounces.
mass of gold in the coin = 30.0924g / (31.1 g/oz.) = 0.967601 troy oz.
Now we can find the value of that much gold before the price change:
Price = 0.967601 troy oz. * .00/troy oz. = .35202
Rounding to three significant digits: .40
That's how much the twenty-dollar gold piece was worth before the price change. .40. Weird, huh?
Anyway, after the price change, the U.S. was no longer on the gold standard. A coin was now worth whatever they said it was worth, instead of how much the gold inside it was worth. So a twenty-dollar gold piece was worth .... exactly twenty dollars. Always and forever. This is a trick question; your classmates will figure the value of the gold after the price change, but that's not what the question asks.
For part b:
You need to figure out the how many cubic centimeters is 2.00 cubic inches:
1 in = 2.54 cm
1 in^2 = 6.4516 cm^2
1 in^3 = 16.387064 cm^3
2 in^3 = 32.774128 cm^3
The density of gold is 19.3g/cm^3. Multiplying by the value above, we get:
19.3g/cm^3 * 32.774128 cm^3 = 632.5406704g. There are about 632.5 grams in 2 cubic inches of gold.
We know from part a) that one double eagle uses 30.0924g of gold. How many times can we cut 30.0924g of gold from a 632.5406704g block?
632.5406704g / 30.0924g = 21.0199476~
That little bit left over is probably due to rounding error, so the answer is 21 coins.
Give your answer to this question below!
[wprebay kw="1933+gold+double+eagle" num="12" ebcat="11116"]
[wprebay kw="1933+gold+double+eagle" num="13" ebcat="11116"]
[wprebay kw="1933+gold+double+eagle" num="14" ebcat="11116"]
Originally posted 2010-10-18 05:36:42. Republished by Blog Post Promoter