If the density of fool's gold is 15.47 and the density of your sample is 15.47, then your sample is possibly 100% fool's gold and 0% pure gold. (Not likely. See below.)

This source lists the density of fool's gold as being between 4.95 and 5.10. If we suppose it is 5.00 and pure gold has a density of 19.31, we can write an equation for x, the fraction of gold in your sample.

19.51x + 5.00(1-x) = 15.47

19.51x + 5.00 - 5.00x = 15.47 (use the distributive property to eliminate parentheses)

14.52x + 5.00 = 15.47 (collect x terms)

14.52x = 10.47 (subtract 5.00)

x = 10.47/14.52 ≈ .7317 (divide by the x coefficient and evaluate)

Your sample may contain 73% gold.

You will note in the reference above that gold and fool's gold are not usually found together. When they are, the proportion of gold is usually much less than 1%. In order to solve the problem, we needed to know the density of each of the components of the mixture.

This source lists the density of fool's gold as being between 4.95 and 5.10. If we suppose it is 5.00 and pure gold has a density of 19.31, we can write an equation for x, the fraction of gold in your sample.

19.51x + 5.00(1-x) = 15.47

19.51x + 5.00 - 5.00x = 15.47 (use the distributive property to eliminate parentheses)

14.52x + 5.00 = 15.47 (collect x terms)

14.52x = 10.47 (subtract 5.00)

x = 10.47/14.52 ≈ .7317 (divide by the x coefficient and evaluate)

Your sample may contain 73% gold.

You will note in the reference above that gold and fool's gold are not usually found together. When they are, the proportion of gold is usually much less than 1%. In order to solve the problem, we needed to know the density of each of the components of the mixture.