How can you explain that the ratio of the densities of Ag and Au equals the ratio of their relative masses?

Question

My book says that silver and gold both have the same face centered cubic structure and then asks to show and explain why the ratio of their densities equals the ratio of their relative masses. How can I do this?

Answer 1

The expression for density of any crystal structure with regular arrangement(fcc, hcp, bcc structure) can be derived as follows

Now to prove what you stated you may have to assume/approximate that Gold and Silver unit cells have the same edge length.