In a class of 60 students, 30 liked mathematics, 35 liked English and 5 like neither of the two subjects. Represent the information in a Venn diagram. Find
A. How many liked both subjects
B. How many liked only one subject
To represent the information in a Venn diagram, draw two overlapping circles. Label one circle "Mathematics" and the other circle "English".
a. Let the number of students who like both subjects be x.
b. Let the number of students who like only mathematics be y.
c. Let the number of students who like only English be z.
d. Let the number of students who like neither subject be 5.
Now we can fill in the information:
30 students like mathematics, so we can write y + x = 30.
35 students like English, so we can write z + x = 35.
5 students like neither subject, so we can write y + z + x = 5.
Adding the three equations together, we have 2x + 2y + 2z = 70.
Dividing by 2, we get x + y + z = 35.
So, there are 35 students who like either mathematics, English, or both.
To find the number of students who like both subjects (A), we can use the equation x + y + z = 35.
Since y + z + x = 5, we get x = 35 - 5 = 30.
Therefore, 30 students liked both mathematics and English.
To find the number of students who liked only one subject (B), we can subtract the value of x from the total number of students who liked either mathematics or English.
This gives us 35 - 30 = 5.
Therefore, there are 30 students who liked both subjects and 5 students who liked only one subject.