First of all, let us assign variables to represent the given. Let us make
s = the smallest package
h = heaviest package
Next, we translate the given into mathematical terms
"the smallest package weighed only 1/3 more than 1/2 the weight of the heaviest package" can be represented as
s = 1/2*h + 1/3
Since the given also stated that the sum of the two packages is 100 kg
s + h = 100 which can be written as
h = 100-s
We have two unknowns and two equations, so this problem can be solved.
Substituting the second equation to the first equation yields
s = 1/2(100-s) + 1/3
s = 50-(1/2)s+(1/3)
s+(1/2)s = 50+(1/3)
(3/2)s = (151/3)
s = 302/9 = 33.56 kg
The smaller package weighed 33.56 kg.
