word problems to solve
Mathematics

Tutor: None Selected  Time limit: 1 Day 
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?
Overview: We will write two equations that contain the information presented and then use subsitution to solve for the weight of the smaller package.
First we'll designate variables to the two packages:
Call the mass of the smaller package x
Call the mass of the larger package y
We know the mass of the two packages add up to 100 kg, so we can write...
x+y = 100
Also, we know that The smallest package weighed only 1/3 more than 1/2 the weight of the heaviest package.
More than suggests the mathematical operation of addition.
of suggests the mathematical operation of multiplication.
For the second equation we write...
x = 1/2 y + 1/3 y
Getting a common denominator we get...
x = 3/6 y + 1/6 y
x = 4/6 y
Now we substitute the above equation for x in terms of y into the equation x + y =100...
4/6 y + y = 100
Getting a common denominator we get...
4/6 y + 6/6y = 100
10/6 y =100
y = 600/10
y = 60 kg
Therefore, since y=60, and we know x+y=100, then...
x = 40 kg
I hope that helps. Let me know if you have any questions or need clarifications on any step.
Steve
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