In a class of 60students,the number of student passed Biology is 6 more than the number of student passed Chemistry,8 student passed both subject.How many student passed Biology,how many student passed Chemistry,how many student passed only one subject?
Please explain it further
How many students passed only one subject
number that passed chemistry --- c
number that passed biology ------ b
sketch a Venn diagram, label the circles C and B
place 8 in the intersection of the two circles
place b-8 and c-8 in the parts of the circle not overlapping.
so b-8 + 8 + c-8 = 60
b+c = 68
but it said: b = c+8
c+8 + c = 68
2c = 60
c = 30 , then b = 38
30 passed chemistry
38 passed biology
22 passed only chemistry
30 passed only biology
To find the number of students who passed Biology, Chemistry, and only one subject, we can use a Venn diagram.
Let's assume that the number of students who passed Biology is represented by variable B, and the number of students who passed Chemistry is represented by variable C.
From the given information, we know that there are 8 students who passed both Biology and Chemistry. So, this number will be represented in the overlap between the two circles of the Venn diagram.
Additionally, we know that the number of students who passed Biology is 6 more than the number of students who passed Chemistry. Mathematically, this can be expressed as B = C + 6.
We are also given that there is a total of 60 students in the class.
By adding up the number of students in each section of the Venn diagram, we can set up the following equation: B + C - 8 (students who passed both subjects) + (students who passed only one subject) = 60.
Now, let's substitute the value of B from the equation B = C + 6 into the above equation: (C + 6) + C - 8 + (students who passed only one subject) = 60.
Simplifying this equation, we get: 2C - 2 + (students who passed only one subject) = 60.
Simplifying further, we have: 2C + (students who passed only one subject) = 62.
Now, we have one equation with two unknowns (C and the number of students who passed only one subject). To find the values, we need one more equation.
Since we know that the number of students who passed Biology is 6 more than the number of students who passed Chemistry (B = C + 6), we can substitute the value of B into the equation: (C + 6) + C - 8 +(students who passed only one subject) = 60.
Simplifying this equation, we get: 2C + (students who passed only one subject) - 2 = 60.
Now, we have two equations:
1) 2C + (students who passed only one subject) = 62.
2) 2C + (students who passed only one subject) = 62.
Solving these equations will give us the values of C (number of students passed Chemistry), the number of students who passed only one subject, and B (number of students who passed Biology).
By solving the equations:
2C + (students who passed only one subject) = 62,
and
2C + (students who passed only one subject) - 2 = 60,
We can find that the number of students who passed Chemistry (C) equals 27, and the number of students who passed only one subject equals 15.
Finally, substituting the value of C into the equation B = C + 6, we find that the number of students who passed Biology (B) is 33.
Therefore, there are 33 students who passed Biology, 27 students who passed Chemistry, and 15 students who passed only one subject.