Math 325                                          Name                 KEY
Quiz 2-A

1. Suppose that there were 56 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 2 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.

 

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 56 jelly beans altogether, p+j+q=56

and, since Peter had 4 times as many as Jerry, p=4j

and, since Peter had 2 fewer than Pam, p=q-2.

We may rewrite p=q-2 as q=p+2.

Now, substituting (q=p+2) into the very first equation, we have

p+j+(p+2)=56.

Substituting (p=4j) into this equation, we have

4j+j+(4j+2)=56.

9j+2=56

9j=54

j=6

Thus, Jerry had 6 jelly beans.  Since p=4j=24,

Peter had 24 jelly beans.


 
 
2. List all of the subsets of the set {2,a}.

 

{},{2},{a},{2,a}


 
3. List all of the elements of the set {x+10 | x Î N and 3 £ x < 8}.

 

{13,14,15,16,17}


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

 
1. {4}

 

1


 
2. {a,b,c,¼,y,z}

 

26


 
3. Æ

 

0


 
4. N

 

¥

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On 14 Sep 2001, 16:07.