A survey of 220 families showed that 83 had
a dog, 64 had a cat, 28 had a dog and cat,
84 had neither a dog nor a cat nor a
parakeet, 6 had a dog, cat and parakeet.
How many only had a parakeet. please solve,
and I am confused. Thank you.
e = number who had a dog but no cat and no parakeet.
f = number who had a dog and a cat but no parakeet.
g = number who had a cat but no dog and no parakeet.
h = number who had a dog and a parakeet but no cat.
i = number who had a dog, a cat, and parakeet.
j = number who had a cat and a parakeet but no dog.
k = number who had a parakeet but no dog and no cat.
l = number who had no dog, no cat, and no parakeet.
We are to find k.
84 had neither a dog nor a cat nor a parakeet,
6 had a dog, cat and parakeet.
So we fill in l=84, and i=6
28 had a dog and cat,
We have already accounted for 6 of these 28
who had all three pets. So the number who
had only a dog and cat but no parakeet is
found by subtracting the 6 from the 28, so
f=28-6=22, so we fill 22 for f:
83 had a dog
We have accounted for 22+6 or 28 dog owners,
and since this is all we are told about dog
owners, all we know is that between e and h
there are 83-28 or 55 dog owners that either
do or don't own a parakeet. So let's leave h
unknown and express e in terms of h as 55-h,
so we leave h unknown and put 55-h for e.
---
64 had a cat
We have accounted for 22+6 or 28 cat owners,
and since this is all we are told about cat
owners, all we know is that between g and j
there are 64-28 or 36 cat owners that either
do or don't own a parakeet. So let's leave j
unknown and express g in terms of j as
36-j, so we leave j unknown and put 36-j for
g.
The only other thing we are given is:
A survey of 220 families
So we add up the numbers or expressions in
all 8 regions and get:
(55-h)+22+(36-j)+h+6+j+k+84 = 220
Simplifying:
55-h+22+36-j+h+6+j+k+84 = 220
203+k = 220
k = 17
Answer: 17
Edwin