Problem: an empty wooden vessel weighs 20 % 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 .
Rationale: an empty wooden vessel weighs 20 % of its total weight when filled with paint : vessel = 0.2 ( vessel + paint ) ; 20 v = v + p ( so the weight of completely filled vessel is 10 v ) p = 19 v ( so the weight of the paint when the vessels is completely filled is 19 v ) . the weight of a partially filled vessel is one half that of a completely filled vessel : v + p ' = 1 / 2 * 20 v ; p ' = 9 v ( so the weight of the paint when the vessels is partially filled is 9 v ) . what fraction of the vessel is filled ? so , we need to find the ratio of the weight of the paint when the vessel iscompletely filledto the weight of the paint when the vessel ispartially filled : p ' / p = 9 v / 19 v = 9 / 19 . answer : d .
annotated_formula: divide(subtract(divide(20, const_2), const_1), subtract(20, const_1))