42 students took a test in school where the passing score was 70. the mean score of the 42 students taking the exam was 75.5 while the mean score of the students who passed the test was 81, and the mean score of the students who failed was 60. How many students passed the test?
To find out how many students passed the test, we need to analyze the given information.
We know that the passing score is 70, and the mean score of all 42 students is 75.5.
First, let's find the total score of all the students. We can do this by multiplying the mean score by the number of students:
Total score = Mean score * Number of students
Total score = 75.5 * 42
Total score = 3171
Now let's find the total score of the students who passed and the students who failed.
Let's assume the number of students who passed is x.
According to the given information, the mean score of the students who passed is 81. So, the total score of the students who passed is:
Total score of students who passed = Mean score of passed students * Number of passed students
Total score of students who passed = 81 * x
Similarly, the total score of the students who failed is:
Total score of students who failed = Mean score of failed students * Number of failed students
Total score of students who failed = 60 * (42 - x)
Since the total score of all the students is the sum of the total score of the students who passed and the total score of the students who failed, we can write the equation:
Total score = Total score of students who passed + Total score of students who failed
3171 = 81x + 60(42 - x)
Now we can solve this equation to find the value of x (number of students who passed):
3171 = 81x + 2520 - 60x
651 = 21x
x = 651/21
x ≈ 31
So, approximately 31 students passed the test.