Of 480 consumers polled, some purchase ice cream, some purchase frozen yogurt, and some purchase both. If 260 people polled purchase ice cream and 200 purchase both ice cream and frozen yogurt, how many people purchase frozen yogurt?

Question

Of 480 consumers polled, some purchase ice cream, some purchase frozen yogurt, and some purchase both. If 260 people polled purchase ice cream and 200 purchase both ice cream and frozen yogurt, how many people purchase frozen yogurt?

Answer 1

Assuming that of the 480, everybody had either ice cream or yogurt

number for ice cream --- A
number for yogurt ---- B

N( A or B) = N(A) + N(B) - N(A and B)
480 = 260 + N(B) - 200
N(B) = 420

confirm the answer is corrrect by making a Venn diagram.

Answer 2

n+260-200 = 480

n = 420

420 bought just yogurt

Answer 3

To determine how many people purchase frozen yogurt, we can use the information given in the question.

First, we know that 260 people purchase ice cream, and 200 of those people also purchase frozen yogurt. This means that the remaining 60 people who purchase ice cream do not purchase frozen yogurt.

Next, we need to determine how many people purchase frozen yogurt exclusively. To do this, we subtract the number of people who purchase both ice cream and frozen yogurt (200) from the total number of people who purchase frozen yogurt.

Therefore, the number of people who purchase frozen yogurt exclusively is 480 - 200 = 280.