in a class of 60 student, the number of student who passed biology is 6 more than the number of student who passed chemistry. Every student passed at least one of the two subject and 8 student passed both subject.
1)how many student passed biology?
2)how many student passed chemistry?
3)how many student passed only one subject
If b passed biology, and c passed chemistry, you know that
b+c-8 = 60
b = c+6
See what you can do with that.
To find the answer to these questions, you can use a method called "Venn diagram" or basic set theory.
Step 1: Draw a Venn diagram with two overlapping circles, one for Biology and one for Chemistry.
Step 2: Label the overlapping region (where the circles intersect) as the number of students who passed both subjects.
Step 3: Let's assume the number of students who passed Biology only is "x" and the number of students who passed Chemistry only is "y".
Step 4: Fill in the diagram with the given information:
- The number of students who passed both subjects is 8.
- The number of students who passed Biology is 6 more than the number who passed Chemistry.
- Every student passed at least one subject, which means you have to add up all the numbers inside the circles and the overlapping region. This sum should be equal to the total number of students, which is 60.
Now let's solve the questions:
1) To find the number of students who passed Biology, you need to add the number of students who passed both subjects (8) and the number of students who passed Biology only (x). Since the number of students who passed Biology is 6 more than Chemistry, you can express it as x = (number of students who passed Chemistry) + 6.
2) To find the number of students who passed Chemistry, you can use the information from the previous question. Since x = (number of students who passed Chemistry) + 6, you can substitute x with (number of students who passed Chemistry) + 6.
3) To find the number of students who passed only one subject, you need to find the sum of the students who passed Biology only (x) and the students who passed Chemistry only (y).
By solving these equations simultaneously, you can find the answers to these questions.