Help with this Physics problem (Fluids)

I'm currently learning about fluids in my physics class but I have no clue where to even begin with this problem. It reads:

"A solid chunk of iron (7.8 x 10^3 kg/m^3) is floating in mercury (13.6 x10^3 kg/m^3). What percentage of the iron object is submerged?"

This question basically asks for a simple force balance on the chunk of iron. There are 2 dominant forces acting on the floating chunk of iron: buoyant force resulting from the displacement of a volume of mercury, and the gravitational force acting on the chunk of iron (ie. its weight).

The gravitational force on the iron chunk is given by F = mg = rho1*(V1)g, where rho1 is the density of the iron and V1 is the volume of the iron chunk. Since the chunk of iron is floating and therefore stationary, this gravitational force must completely cancel out the buoyant force due to the displaced mercury. Buoyant force is given by F = rho2*(V2)g, where rho2 is the density of the fluid (ie mercury) and V2 is the volume of fluid displaced, which is equivalent to the submerged volume of the iron chunk.

Using a force balance, we get:
F = rho1*(V1)g = rho2*(V2)g

Simplifying:
rho1*V1 = rho2*V2
V2/V1 = rho1/rho2

Substituting in the density values:
V2 = V1*(7.8/13.6) = 0.5735*V1

Thus, we get the final answer: 57.35% of the iron chunk is submerged.