SOLUTION: 2) At a local kennel there are 800 dogs staying over the March Break. Of these dogs, 518 are male, 212 are brown and 375 are puppies. 247 are male puppies, 143 are brown puppies an

The clues are:

1. 800 dogs
2. 518 are male
3. 212 are brown
4. 375 are puppies 
5. 247 are male puppies
6. 143 are brown puppies 
7. 107 are brown males
8.  68 are brown male puppies 

Question: Females who are older and not brown? 

Draw a Venn Diagram. Draw three overlapping circles inside a rectangle.
Label the circles M, B, and P for "male", "brown" and "puppy".  Put letters
(equal to a question mark) for the number of dogs in each of the 8 regions.
I chose the letters s through z.



s is in circle M but not in circles B or P
So s = the number of males that are not brown but not puppies.

t is in circles M and B but not in circle P
So t = the number of males that are brown but not puppies.

u is in circles B and P but not in circle M
So u = the number of brown dogs that are puppies but male.

v is in circles M and P but not in circle B
So v = the number of male dogs that are puppies but not brown.

w is in circles M, B, and P.
So w = the number of males that are brown and puppies.

Usually in these Venn diagram problems 
the clues are given in reverse order from
the order you need to work them in.
So I will reverse them

 
8. 68 are brown male puppies.  That says w = 68
   So fill in w=68 on the Venn diagram
7. 107 are brown males.        That says t+w = 107
   From that we get that t = 107-w = 107-68 = 39.
   So fill in t=39 on the Venn diagram.  
6. 143 are brown puppies       That says x+w = 143
   From that we get that x = 143-w = 143-68 = 75.
   So fill in x=75 on the Venn diagram.
5. 247 are male puppies        That says v+w = 247
   From that we get that v = 247-w = 247-68 = 179.
   So fill in v=179 on the Venn diagram.   
4. 375 are puppies             That says v+w+x+y = 375
   From that we get that y = 379-v-w-x = 375-179-68-75 = 53
   So fill in y=53 on the Venn diagram.
3. 212 are brown.              That says t+u+w+x = 212
   From that we get that u = 212-t-w-x = 212-39-68-75 = 30
   So fill in u=30 on the Venn diagram.
2. 518 are male                That says s+t+v+w = 518
   From that we get that s = 518-t-v-w = 518-39-179-68 = 232
   So fill in s=232 on the Venn diagram.
1. 800 dogs                    That says s+t+u+v+w+x+y+z = 800
   From that we get that z = 800-s-t-u-v-w-x-y = 
   800-232-38-30-179-68-75-53 = 124
   So fill in z=124 on the Venn diagram.



Now we're ready to answer the question:

How many of the dogs are females who are older and not brown?

Since they are females they are not males so they are not in M
Since they are older they are not puppies so they are not in P
Since they are not brown they are not in B
So they are the ones who are not in any of the circle, so
the question is asking "What is z?"

Answer: 124

Edwin