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's assume the weight of the smaller package as "x" kilograms.
According to the given information, the weight of the heaviest package is 100 - x kilograms.
Given that the weight of the smallest package is only 1/3 more than 1/2 the weight of the heaviest package, we can write the equation:
x = (1/2)(100 - x) + (1/3)(100 - x)
Multiplying through by 6 to eliminate the fractions:
6x = 3(100 - x) + 2(100 - x)
Simplifying the equation:
6x = 300 - 3x + 200 - 2x
Combining like terms:
11x = 500 - 5x
Bringing the "x" terms to one side and the constant terms to the other:
11x + 5x = 500
16x = 500
Dividing both sides by 16:
x = 500/16
x ≈ 31.25
Therefore, the weight of the smaller package is approximately 31.25 kilograms.
To solve this problem, we need to set up and solve an equation.
Let's assume the weight of the smaller package is x kilograms. According to the problem, the smallest package weighed only 1/3 more than 1/2 the weight of the heaviest package. So, the weight of the heaviest package would be 2/3 of the weight of the smaller package.
Now, we can set up the equation:
Weight of smaller package + Weight of heaviest package = Total weight
x + (2/3)x = 100
To solve the equation, we can combine the like terms:
(5/3)x = 100
Next, we isolate x by multiplying both sides of the equation by the reciprocal of 5/3 (which is 3/5):
x = (100 * 3/5)
Now, let's calculate the value of x:
x = 60
Therefore, the smaller package weighs 60 kilograms.