Basic buoyancy problem, as you found out.
The force reduction (buoyancy force) is equal to the weight of the displaced water, but since you're not given volume you're given the force, you need to solve for the volume.
Now you have the volume of the crown, and you know the total weight, so find the total density of the crown.
Then use x vs (1-x) to figure out the ratio of densities, etc.