Buoyant Force problem?

Question

A piece of metal weighs 50 N in air, 36 N in water and 41 N in oil. Find the density of the metal and the density of the oil when the metal is completely submerged in both water and oil.

Answer 1

Given
W(metal) = 50N
Fb (water)=36N
Fb (oil)=41N

Fb (water)=g(p(metal) - p(water))V (1)

Fb (oil)=g(p(metal) - p(oil))V (2)

p(metal) = W(metal)/(gV) (3)

Substituting (3) in to (1) we have
Fb (water)=g(W(metal)/(gV) - p(water))V
Fb (water)=(W(metal)- gV p(water)
V=[Fb (water)-(W(metal)]/[g p(water)]

then substitute (3) into (2) we have

Fb (oil)=g(W(metal)/(gV) - p(oil))V

P(oil)=[ Fb (oil)- W(metal) ]/V

and from (3)

p(metal) = W(metal)/(gV)

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