word problems to solve

label Mathematics
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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? 

May 20th, 2015

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


May 20th, 2015

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