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?
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
To solve this problem, we'll use algebra to represent the information given. Let's denote the weight of the smaller package as 'x' (in kilograms) and the weight of the heaviest package as 'y' (in kilograms).
From the given information, we know that the smallest package weighed only 1/3 more than 1/2 the weight of the heaviest package. Mathematically, we can write this as:
x = (1/2)y + (1/3)(1/2)y
Simplifying this equation, we have:
x = (1/2)y + (1/6)y
Combining the like terms on the right side, we get:
x = (3/6)y + (1/6)y
x = (4/6)y
x = (2/3)y
We also know that the combined weight of both packages is 100 kilograms. So, we can write another equation:
x + y = 100
Now, we have a system of two equations:
x = (2/3)y
x + y = 100
To solve for x, we can substitute the expression for x in terms of y into the other equation:
(2/3)y + y = 100
Adding the fractions and simplifying, we have:
(5/3)y = 100
To isolate y, we can multiply both sides of the equation by the reciprocal of (5/3), which is (3/5):
y = 100 * (3/5)
y = 60
Now, we can substitute the value of y back into one of the equations to find x:
x = (2/3)y
x = (2/3)(60)
x = 40
Therefore, the smaller package weighs 40 kilograms.
Let's assume the weight of the smaller package is x kilograms.
According to the given information, 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 (1/2)x + (1/3)x = (5/6)x kilograms.
The two packages combined weighed 100 kilograms.
So, the equation becomes x + (5/6)x = 100.
Now, let's solve this equation to find the value of x.
Combining the like terms, we have (11/6)x = 100.
To solve for x, we divide both sides of the equation by (11/6).
x = (100 * 6) / 11
x ≈ 54.545
Therefore, the weight of the smaller package is approximately 54.545 kilograms.