Question

A survey of 70 people found that 50 people like coffee, 25 like tea, and 13 like both.How many people like coffee or tea, or both?

Answer 1

Explanation:

your question is strange.

first you tell us that 50 people like coffee, 25 like tea, and 13 like both.

and then you ask how many like coffee or tea or both.

is this a joke ? or do you rather mean how many like only coffee, or only tea, and how many don't like neither ?

since 13 people like coffee and tea, these 13 are also part of the group of 50 that like coffee, and of the group of 25 that like tea.

so, to get the number of people that like only one, we need to deduct the number of people, who like both from both groups.

the number of people that only like coffee is therefore

50 - 13 = 37

and the number of people that only like tea is

25 - 13 = 12

we know the number of people that like coffee and tea is 13.

together that are

37 + 12 + 13 = 62 people.

that means 70 - 62 = 8 people don't like neither coffee nor tea.

Answer 2

Answer: 62

Explanation:

Those who like coffee only = 50 - 13 = 37. Those who like tea only = 25 - 13 = 12. Those who like either coffee, or tea, or both = 37 + 12 + 13 = 62.

In theory, the 70 people being surveyed could fall under any of the following four categories:

1. Those who like coffee,
2. Those who like tea,
3. Those who like both coffee and tea,
4. Those who like neither coffee nor tea.

I have labelled the four categories 1, 2, 3 and 4 for convenient reference.

From the information provided in the question, category 1 contains 50 people, category 2 contains 25 people, while category 3 contains 13 people. We do not yet know how many people fall under category 4, but we shall calculate it.

We know from set theory that the four aforementioned categories are known formally as sets. A set is simply a group of objects or things that are similar in some way. Each of the objects in a set is called a member of that set. Two sets can intersect. The intersection of two sets is simply the collection of members that are in both of the two sets. Also, two sets can unite. The union of two sets is the collection of members that in either of the two sets.

For example, category 3 is the intersection of category 1 and 2. The question requires us to calculate the union of category 1 and 2.