Question

In one hour at Pete’s Pet Store, 25 customers bought items. 12 customers bought items for dogs, and 5 of those customers also bought items for cats. If 4 customers bought items for neither dogs nor cats, how many people bought items for cats only? (Hint: On a piece of paper, draw a Venn diagram to represent the situation) A. 5 B. 7 C. 9 D. 14

Answer 1

Answer: Option 'C' is correct.

Step-by-step explanation:

since we have given that

Let A be those customers who bought items for dogs

Let B be those customers who bought items for cats

So, we have:

$n(U)=25\\\\n(A)=12\\\\n(A\cap B)=5\\\\n(A\cup B)'=4$

As we know that

$n(A\cup B)=n(U)-n(A\cup B)'\\\\n(A\cup B)=25-4\\\\n(A\cup B)=21$

Now, we will use the "Formula for sets":

$n(A\cup B)=n(A)+n(B)-n(A\cap B)\\\\21=12+n(B)-5\\\\21=7+n(B)\\\\21-7=n(B)\\\\14=n(B)$

Now, we want number of people bought items for cats only:

$n(\text{only cat)}=n(A)-n(A\cap B)\\\\n(\text{only cat)}=14-5\\\\n(\text{only cat)}=9$

Hence, there are 9 people who bought items for cats only.

Therefore, Option 'C' is correct.

Answer 2

C.9
why?because from 25 customers 12 bought for dogs and 4 bought for neither so
25=12+4+x
x representing the ones that only bought for cat
25=16+x
-16 both sides
9=x