The smallest package weighed only 1/3 more than 1/2 the weight of the heaviest package. If the two packages combined weighed 100 kilograms, how much did the smaller package weigh?

Answer 1

heavy package = x
small = (4/3)(x/2) = 2x/3

2x/3 + x = 100
times 3
2x + 3x = 300
5x = 300
x = 60

heavy one --- 60 kg
small one -- - 40

Check:
half the weight of the heavy one is 30 kg
a third of that is 10 kg
a third more than 1/2 the heavey = 10 + 30 = 40
-- all looks good