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This is my attempt:

Weight of object in ethyl alcohol [Woe]= (density of alchohol[de])(volume of object)(gravity)

Weight of object in water[Wow] = (densityof water[dw])(volume of object)(gravity)

therefore:

Woe/de = Wow/dw

Woe/Wow = de/dw

15.2/13.7 = de/dw

but this is where i get stuck..because both the equations have volume and gravity they just cancel and i can't solve for either of the densities...

thanks for any hints..