In a house of 60 adult,4 of them are both farmers and teachers.30 of them are only farmers and 10 of them do not work.
a. Find the number of farmers in house
b. represent the information on a Venn diagram
c. Find the number of adult in the house who are;
Teachers only
In only one profession
Teachers
To solve this problem, we can use the principle of inclusion-exclusion. We will start with the given information and work our way to find the answers to the questions.
a. Let's start by finding the total number of farmers in the house.
Since 30 of them are only farmers and 4 are both farmers and teachers, we can add these two numbers together:
Number of farmers = 30 + 4 = 34
b. Now, we will create a Venn diagram to represent the information given.
Let's denote "F" as the set of farmers and "T" as the set of teachers.
The overlapping region will represent the people who are both farmers and teachers.
| T |
|--------|
| 4 |
|------|--------|------|
| 30 | x | | - Represents the farmers' only set
|------|--------|------|
| 10 | | - Represents the people who do not work
As we can see, the total number of adults in the house is 60. Therefore, the number of adults who are neither farmers nor teachers is:
60 - 10 = 50
c. Now, let's find the number of adults who are teachers only.
To find this, we need to subtract the number of people who are both farmers and teachers from the total number of teachers:
Number of teachers only = Total number of teachers - Number of people who are both farmers and teachers
Number of teachers only = 60 - 4 = 56
To find the number of adults who are in only one profession, we need to add the number of adults in the overlapping region to the number of adults who are neither farmers nor teachers:
Number of adults in only one profession = Number of adults in the overlapping region + Number of adults who do not work
Number of adults in only one profession = 4 + 50 = 54
To find the number of teachers, we need to add the number of adults who are both farmers and teachers to the number of adults who are teachers only:
Number of teachers = Number of adults who are both farmers and teachers + Number of adults who are teachers only
Number of teachers = 4 + 56 = 60
Therefore, the final answers are:
a. Number of farmers in the house = 34
b. Venn diagram representation is shown above.
c. Number of adults in the house who are teachers only = 56
Number of adults in the house who are in only one profession = 54
Number of adults in the house who are teachers = 60