Use Venn Diagram to answer this question The new owner of a

Use Venn Diagram to answer this question

The new owner of a student apartment building near campus was considering establishing a No Pets rule. He decided to survey the current residents to see how many owned pets and what kind of pets they owned. The building had 58 units. The previous owner had not allowed cats or dogs or other mammals, but the residents reported a variety of other pets: 30 owned birds, 38 owned fish, and 30 owned frogs, lizards, or snakes. Of those how had fish, 19 also had a frog, lizard, or snake.The owner found that 18 had both fish and birds and 15 kept a bird and a frog, lizard, or snake. Lastly, he determined that 10 owned fish, abird, lizard, or snake. How many residents could have reported no pets? How many residents owned a bird but not a fish? How many residents do not own a bird?

Solution

consider the term resident refers to ALL occupants of a single unit. That is, even if four people live in a unit, they are considered ONE resident.

Second, we have to assume all 58 units are occupied, that there are no vacant units.

B=Bird
F=Fish
S=Frog/Lizard/Snake

Let\'s do this bottom-up eliminate double counting.

10 owned FBS (we keep this number)

It says 15 owned BS. However, 10 of these are FBS, so
5 owned BS (no F, we keep this number)

It says 18 owned FB. However, 10 of these are FBS, so
8 owned FB (no S, we keep this number)

It says 19 owned FS. However, 10 of these are FBS, so
9 owned FS (no B, we keep this number)

It says 30 owned B. However, 10 are FBS; 8 are FB; 5 are BS so
7 owned B (no other critters, so we keep this number)

It says 38 owned F. However, 10 are FBS; 8 are FB; 9 are FS so
11 owned F (no other critters, so we keep this number)

It says 30 owned S. However, 10 are FBS; 5 are BS; 9 are FS so
6 owned S (no other critters, so we keep this number)

The total residents with pets are:
10+5+8+9+7+11+6 = 56

two units have no pets.