Empty.................. Paint............... Total

Say total weight when completely filled with paint = 100

10....................... 90 .................. 100

Say x quantity paint is removed

10 .......................... 90-x............. 100-x

Equation would come up as

\(\frac{1}{2} * 100 = 100-x\)

x = 50

90 - x = 90 - 50 = 40

Fraction \(= \frac{40}{90} = \frac{4}{9}\)

Answer = D
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An empty wooden vessel weighs 10% of its total weight when filled with paint. If the weight of a partially filled vessel is one half that of a completely filled vessel, what fraction of the vessel is filled.

A. 3/5
B. 5/9
C. 1/24
D. 4/9
E. 2/5

v=weight of empty vessel
p=weight of paint in full vessel
v+p=10v=total weight of full vessel
p=9v
let x=fraction of p remaining after total weight of full vessel is halved
v+9vx=5v
x=4/9
D

We can let the weight of the vessel when it’s filled with paint = 100, so the vessel itself weighs 10 and the paint weighs 90. If a partially filled vessel is one-half the weight of a completely filled vessel, then the partially filled vessel weighs 50. Since the vessel itself still weighs 10, the paint weighs 40. Since a completely filled vessel can be filled with paint that weighs 90, a partially filled vessel with paint that weighs 40 is 40/90 = 4/9 of a completely filled vessel with paint.

Answer: D
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