in a class of 60 student,64 passed biology and 42 passed chemistry.every student passed at least one of the two subjects.How many student passed in both subject?
Please proofread your question.
How can 64 out of 60 students pass biology?
42 - both = chem alone
64 - both = bio alone
chem alone + bio alone + both = 60
both = b
chem alone = c
bio alone = d
so
42 - b = c
64 - b = d
-------------subtract
-22 = c-d
c+d+b = 60
c+ b = 42
-----------------subtract
d = 18
then b = 64 - d = 46
NOTE - impossible BECAUSE you have a typo
In a class of 60, 64 did NOT pass biology :)
However this is how to do it when you get it right.
To find out how many students passed in both subjects, we need to use the concept of set intersection.
Given that 64 students passed biology and 42 students passed chemistry, we can represent these two sets as follows:
- Set A represents the students who passed biology: A = {64}
- Set B represents the students who passed chemistry: B = {42}
Now, to determine the number of students who passed in both subjects, we take the intersection of sets A and B. In other words, we need to find the common elements between the two sets. Mathematically, this can be represented as: A ∩ B.
To calculate the intersection between the two sets, we need to subtract the total number of students who passed both subjects from the total number of students who passed either subject.
Given that every student passed at least one of the two subjects, the total number of students who passed either subject (union of sets A and B) is the sum of the number of students who passed biology (A) and the number of students who passed chemistry (B), minus the number of students who passed both subjects (A ∩ B).
So, let's calculate the number of students who passed in both subjects:
Total students passed either subject = |A ∪ B|
= |A| + |B| - |A ∩ B|
Total students passed either subject = 64 + 42 - X
= 106 - X
Since the total number of students in the class is 60, we can equate the total number of students passed either subject to 60:
106 - X = 60
Now, we can solve for X, which will give us the number of students who passed both subjects:
X = 106 - 60
X = 46
Therefore, the number of students who passed in both biology and chemistry is 46.