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?

Let the weight of the heaviet package = X

Weight of the smallest package = X/2 + (1/3*X/2)

= X/2+X/6

= 2X/3

Then

X+2X/3 = 100

(3X+2X) / 3 = 100

5X/3 = 100

X = 300/5

= 60

Then the weight of the smallest package = 2X/3

= 2*60/3

= 40

So the weight of the smallest package is 40 Kg.