42 student in class took a test in Science and English.13 students took both subject and 4 students did not pass in any of the two subject.those who Science is 7 less than those who took only English a) illustrate the information on venn diagram (b): find the number of students who passed (i) Science; (ii) English; (iii);exactly one subject
Answer
If you drew your Venn diagram, and labeled E as those who passed only English, then it should be clear that
E-7 - 13 + E = 42-4
Now you can fill in the numbers and answer the questions.
To illustrate the information on a Venn diagram:
Step 1: Draw two overlapping circles to represent the subjects Science and English. Label them accordingly.
Step 2: In the overlapping region of the circles, write the number of students who took both subjects. In this case, it is 13.
Step 3: Outside the overlapping region, write the number of students who only took Science. This value is 7 less than the number of students who only took English.
Step 4: Lastly, write the number of students who did not pass in either subject. In this case, it is 4.
The Venn diagram now represents all the mentioned information.
To find the number of students who passed in each subject:
(i) Science: To find the number of students who passed in Science, we need to subtract the number of students who did not pass in Science from the total number of students who took Science.
Given that 4 students did not pass in either subject, we can calculate the number of students who passed in Science as follows:
Total number of students who took Science = Number of students who only took Science + Number of students who took both subjects
Let's denote the number of students who only took Science as S and the number of students who took both subjects as B.
Total number of students who took Science = S + B
We know that S = (number of students who took only English) - 7
Therefore, S = (total number of students who took English) - (number of students who took both subjects) - 7
Substituting the given values:
S = 42 - 13 - 7
S = 22
Now we can calculate the number of students who passed in Science:
Number of students who passed in Science = Total number of students who took Science - Number of students who did not pass in Science
Number of students who passed in Science = S - 4
Number of students who passed in Science = 22 - 4
Number of students who passed in Science = 18
So, the number of students who passed in Science is 18.
(ii) English: To find the number of students who passed in English, we follow the same steps as above, with the relevant values.
Total number of students who took English = Number of students who only took English + Number of students who took both subjects
Given that the total number of students who took English is 42, we can write:
42 = (number of students who only took English) + 13
Number of students who only took English = 42 - 13
Number of students who only took English = 29
Now, to find the number of students who passed in English:
Number of students who passed in English = Total number of students who took English - Number of students who did not pass in English
Number of students who passed in English = 29 - 4
Number of students who passed in English = 25
So, the number of students who passed in English is 25.
(iii) Exactly one subject: To find the number of students who took exactly one subject, we need to subtract the number of students who took both subjects from the total number of students who took either subject.
Number of students who took exactly one subject = (Total number of students who took Science) + (Total number of students who took English) - (Number of students who took both subjects)
Substituting the given values:
Number of students who took exactly one subject = 18 + 25 - 13
Number of students who took exactly one subject = 30
So, the number of students who took exactly one subject is 30.