In high-school 135 freshmen were interviewed.
Thirty five of them took PE, 42 took BIO, 60 took ENG, 10 took PE and BIO, 15 took PE and ENG, 7 took BIO and ENG, 5 took all three subjects.
1. How many students took none of the three subjects?
2. How many students took PE but not BIO?
3. How many students took ENG but not both BIO and PE?
4. How many students did not take ENG or BIO?
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Ok so I searched through Brainly for this one and saw this, so I wanted to help.
1. 25
2. 25
3. 43
4. 40
I had a fifth problem and a sixth (bonus) problem, you might have this so here it is:
5. 118/135
6. 9
1. 25
2. 25
3. 55
4. 40
the answer is 420.69
proof:
trust the process
How do you do this problem and what's the answer for the last one
To solve these questions, we can utilize the principle of inclusion-exclusion, which is a counting technique that considers overlaps between sets. Let's proceed step by step:
Step 1: Identify the given information:
- Total number of freshmen interviewed: 135
- Number of students taking PE: 35
- Number of students taking BIO: 42
- Number of students taking ENG: 60
- Number of students taking PE and BIO: 10
- Number of students taking PE and ENG: 15
- Number of students taking BIO and ENG: 7
- Number of students taking all three subjects: 5
Step 2: Calculate the number of students taking none of the three subjects (question 1):
To find the number of students taking none of the three subjects, we need to subtract the number of students taking at least one subject from the total number of students interviewed.
First, let's find the total number of students taking at least one subject:
Total students taking PE: 35
Total students taking BIO: 42
Total students taking ENG: 60
Now, let's subtract the number of students taking at least one subject from the total number interviewed:
Total students taking at least one subject = Total students taking PE + Total students taking BIO + Total students taking ENG - Total students taking all three subjects
= 35 + 42 + 60 - 5
= 132
Therefore, the number of students taking none of the three subjects is:
Total number of students interviewed - Total students taking at least one subject
= 135 - 132
= 3
So, 3 students took none of the three subjects.
Step 3: Calculate the number of students taking PE but not BIO (question 2):
To find the number of students taking PE but not BIO, we need to subtract the number of students taking both subjects from the total number of students taking PE.
Total students taking PE: 35
Total students taking PE and BIO: 10
Number of students taking PE but not BIO = Total students taking PE - Total students taking both subjects
= 35 - 10
= 25
Therefore, 25 students took PE but not BIO.
Step 4: Calculate the number of students taking ENG but not both BIO and PE (question 3):
To find the number of students taking ENG but not both BIO and PE, we need to subtract the number of students taking all three subjects and the number of students taking all three subjects from the total number of students taking ENG.
Total students taking ENG: 60
Number of students taking all three subjects: 5
Number of students taking ENG and BIO: 7
Number of students taking ENG and PE: 15
Number of students taking ENG but not both BIO and PE = Total students taking ENG - Number of students taking all three subjects - Number of students taking ENG and BIO - Number of students taking ENG and PE
= 60 - 5 - 7 - 15
= 33
Therefore, 33 students took ENG but not both BIO and PE.
Step 5: Calculate the number of students who did not take ENG or BIO (question 4):
To find the number of students who did not take ENG or BIO, we need to subtract the number of students taking both ENG and BIO from the total number of students interviewed.
Total number of students interviewed: 135
Number of students taking ENG and BIO: 7
Since the question asks for the number of students who did not take ENG or BIO, we need to subtract the number of students taking both subjects from the total number.
Number of students who did not take ENG or BIO = Total number of students interviewed - Number of students taking ENG and BIO
= 135 - 7
= 128
Therefore, 128 students did not take ENG or BIO.
Ok, Thank you!!!
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