Archimedes used density along with mass and volume of alloys (mixtures) of gold and silver to determine the percent of gold (and also silver) in these alloys by simple, non-destructive measurements.

Question

Prove that the mass of gold in a given mass of silver alloy is given by the equation:

MAu= (Malloy-Valloy PAg) * PAu/(PAu-PAg)


You will need to set up two simultaneous equations in two unknowns that include the densities of sliver and gold, and the weight and volume of the alloy!