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Session 4, Part B:
The Mixture Blues

In This Part: Comparing Mixtures | Mixing Blues

Some of the scientists in the lab decided to see what would happen if they took two different mixtures and mixed them together. They called this the "union" of the two mixtures. For example, in Problem B4, they took the two mixtures A and B and formed the union of the mixtures. Standard mathematical notation for the union of two things (usually sets) is U, so they named their new mixture A U B.

Problem B8

Solution  

In this example, which is bluer: A, B, or A U B?

 

Problem B9

Solution  

What can you say about the relative "blueness" of A and B if A U B is bluer than A? If it is bluer than B?

Stop! Do the above problem before you proceed. Use the tip text to help you solve the problem if you get stuck.
Your results from Problems B1-B7 may be helpful here.   Close Tip

 

Problem B10

Solution  

Can A U B ever be bluer than both A and B? If not, why? If so, when? Note 5

Stop! Do the above problem before you proceed. Use the tip text to help you solve the problem if you get stuck.
Consider this problem from a practical standpoint.   Close Tip

 

Problem B11

Solution  

Can A U B ever be just as blue as either A or B? If not, why? If so, when?

 
 

Someone invented a term called the "blueness quotient" (BQ) of a mixture. In the mixture in Problem B4, the BQ of A is 3/5, and the BQ of B is 2/4.

Blueness quotient

 

Problem B12

Solution  

Come up with a rule for computing the BQ of A U B if you know the BQs of A and B.

Take it Further

Problem B13

 Solution  

Mixture A has a BQ of 1/3, and the lab has decided that it would like A U B to have a BQ of 1/2. What could be the BQ of mixture B? Is there more than one answer? Why?

 

Next > Part C: Quadperson

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