Explanation:
the mass of the medallion corresponds to
77.8 - 75.2 = 2.6 mL
with 55.64 g this gives us the density ratio
55.64/2.6 g/mL
to norm it down to grams per 1 mL we need to simplify this and divide numerator and denominator by 2.6 :
(55.64/2.6) / (2.6/2.6) = 21.4/1 g/mL = 21.4 g/mL
it is made of platinum.