In a class of 100 students, 40 failed in Math, 30 failed in Physics, 60 failed in Chemistry. 35 passed in both Math and Physics. 20 passed in Physics and Chemistry. 25 passed in Math and Chemistry. Each student passed in at least one subject. How many students passed in all the subjects?
Well, we have quite the mathematician over here! Let's see if we can solve this puzzle together.
So, we know that 40 students failed in Math, 30 failed in Physics, and 60 failed in Chemistry. We also know that 35 passed in both Math and Physics, 20 passed in Physics and Chemistry, and 25 passed in Math and Chemistry.
Now, let's focus on the overlapping areas. We have the intersection of Math and Physics, which is 35 students. We have the intersection of Physics and Chemistry, which is 20 students. And we have the intersection of Math and Chemistry, which is 25 students.
To find out how many students passed in all three subjects, we need to add up the students who passed in each individual subject.
So, if we add 35 (passed in Math and Physics) + 20 (passed in Physics and Chemistry) + 25 (passed in Math and Chemistry), we get 80.
Therefore, 80 students passed in all three subjects.
I hope I was able to bring a little mathematical laughter to your day!
To find the number of students who passed in all three subjects, we need to use the principle of inclusion-exclusion.
Step 1: Add the number of students who passed in each subject individually.
- Number of students who passed in Math = 100 - 40 = 60
- Number of students who passed in Physics = 100 - 30 = 70
- Number of students who passed in Chemistry = 100 - 60 = 40
Step 2: Subtract the number of students who passed in at least two subjects (double-counted in Step 1).
- Number of students who passed in both Math and Physics = 35
- Number of students who passed in both Physics and Chemistry = 20
- Number of students who passed in both Math and Chemistry = 25
Step 3: Add the number of students who passed in all three subjects.
- Number of students who passed in all three subjects = 35 (from Step 2)
Now, calculate the total number of students who passed in all three subjects by combining the results:
60 + 70 + 40 - 35 - 20 - 25 = 90
Therefore, 90 students passed in all three subjects.