Math 325                                          Name                 KEY
Quiz 2-B
 
  1. Suppose that there were 66 jelly beans in a bowl.  Peter, Jerry and Pam ate all of them.  Peter had four times as many jelly beans as Jerry did and had 3 fewer jelly beans than Pam.  How many jelly beans did Peter eat?  Make sure you correctly introduce all of your variables and clearly show your work.

    2.  

     
    Let p be the number of jelly beans Peter ate. 
    Let j be the number of jelly beans Jerry ate. 
    Let q be the number of jelly beans Pam ate.
    Then, since there are 66 jelly beans altogether, p+j+q=66 
    and, since Peter had 4 times as many as Jerry, p=4j 
    and, since Peter had 3 fewer than Pam, p=q-3.
    We may rewrite p=q-3 as q=p+3. 
    Now, substituting (q=p+3) into the very first equation, we have 
    p+j+(p+3)=66. 
    Substituting (p=4j) into this equation, we have 
    4j+j+(4j+3)=66. 
    9j+3=66 
    9j=63 
    j=7 
    Thus, Jerry had 7 jelly beans.  Since p=4j=28, 
    Peter had 28 jelly beans.

     
     

  2. List all of the subsets of the set {1,b}.

    3.  
    {},{1},{b},{1,b}

     
  3. List all of the elements of the set {x+15 | x Î N and 3 £ x < 8}.

    4.  
    {18,19,20,21,22}

     
  4. State the cardinal number of each of the following sets:

    5.  
    1. {6}

      2.  
      1

       
    2. {a,b,c,¼,y,z}

      3.  
      26

       
    3. Æ

      4.  
      0

       
    4. N

      5.  
      ¥

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On 14 Sep 2001, 16:09.