Answer:
Suppose Archimedes weighed the crown (we'll say 2700 grams)
Then he put the crown on a string and weighed the crown in water and found its weight to be 2560 g.
That means that an equivalent volume of water weighed
2700 - 2560 = 140 grams
Then the density of the crown is 2700 / 140 = 19.3
So this is the density of pure gold and the crown could be considered to be made of pure gold with no other metals in its composition.