Twentyfour dogs are in a kennel. Twelve of the dogs are black, six of the dogs
have short tails, and fifteen of the dogs have long hair. There is only one dog
that is black with a short tail and long hair. Two of the dogs are black with
short tails and do not have long hair. Two of the dogs have short tails and long
hair but are not black. If all of the dogs in the kennel have at least one of the
mentioned characteristics, how many dogs are black with long hair but do not
have short tails?
Draw a Venn diagram to represent the situation described in the problem.
Represent the number of dogs that you are looking for with
x.
•
Notice that the number of dogs in each of the three categories is labeled
OUTSIDE
of the circle in a colored box. This number is a reminder of
the total of the numbers which may appear anywhere inside that
particular circle.
•
After you have labeled all of the conditions listed in the problem, use
this
OUTSIDE
box number to help you determine how many dogs are
to be labeled in the empty sections of each circle.
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Once you have
EVERY
section in the diagram labeled with a number or
an expression, you are ready to solve the problem.
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 Spring '11
 M
 Physics, 5%, 20%, 30%, Long hair, Town X

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