In a class of 60 students,the number of students who passed biology is 6 more than the number who passed chemistry.every student passed at least one of the two subjects and 8 students passed both subjects.
1.How many students passed biology?
2.how many students passed chemistry?
3.how many students passed only one subject?
Let's denote the number of students who passed biology as B and the number of students who passed chemistry as C.
1) We know that the number of students who passed biology (B) is 6 more than the number of students who passed chemistry (C). Therefore, B = C + 6.
2) We are given that 8 students passed both subjects. This means that these 8 students are included in both the number of students who passed biology and the number of students who passed chemistry. Therefore, the number of students who passed only biology is B - 8, and the number of students who passed only chemistry is C - 8.
3) Every student passed at least one of the two subjects. This means that the total number of students who passed biology and the total number of students who passed chemistry should add up to 60. Therefore, B + C - 8 + (C - 8) = 60.
Simplifying this equation, we get B + 2C - 16 = 60.
Now, we can substitute B = C + 6 into the equation to solve for C:
C + 6 + 2C - 16 = 60.
3C - 10 = 60.
3C = 70.
C = 70/3.
However, since the number of students must be a whole number, we need to check if C can be a whole number. Since 70/3 is not a whole number, we need to try a different approach.
We know that the total number of students is 60. Therefore, the number of students who passed only biology (B - 8) plus the number of students who passed only chemistry (C - 8) plus the number of students who passed both subjects (8) should add up to 60.
So, (B - 8) + (C - 8) + 8 = 60.
B - 8 + C - 8 + 8 = 60.
B + C - 8 = 60.
B + C = 68.
We also know that B = C + 6. Substituting this equation into the previous one, we get C + 6 + C = 68.
2C + 6 = 68.
2C= 68 - 6.
2C = 62.
C = 62/2.
C = 31.
Now, we can substitute this value into B = C + 6 to find B:
B = 31 + 6.
B = 37.
Therefore, the answers to the questions are as follows:
1) The number of students who passed biology is 37.
2) The number of students who passed chemistry is 31.
3) The number of students who passed only one subject is (B - 8) + (C - 8) = (37 - 8) + (31 - 8) = 29 + 23 = 52.