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?
Since the mean score of the 42 students was 75.5, the sum of all the scores of all students was 75.5(42)
let the number of students who passed be x
then 42-x must have failed
the sum of the scores of the passing students is then 81x, and
the sum of the scores of the failing students was (42-x)(60)
so isn't 81x + (42-x)(60) = (42)(75.5) ???
Take it from there
To find the number of students who passed the test, we need to compare their scores to the passing score of 70.
We are given that the mean score of the 42 students taking the exam was 75.5. This means that if we add up all their scores and divide by 42, we will get 75.5.
To calculate the total score of the 42 students, we multiply the mean score (75.5) by the total number of students (42):
Total score of the 42 students = 75.5 × 42
Next, we are given that the mean score of the students who passed the test was 81. This means that if we add up their scores and divide by the number of students who passed, we will get 81. However, we don't know the number of students who passed yet, so we'll call it "x".
To calculate the total score of the students who passed, we multiply the mean score (81) by the number of students who passed (x):
Total score of the students who passed = 81x
Similarly, we are given that the mean score of the students who failed was 60. This means that if we add up their scores and divide by the number of students who failed, we will get 60. Since we know there are 42 students in total, and we need to find the number of students who passed, we can calculate the number of students who failed:
Number of students who failed = Total number of students - Number of students who passed
Number of students who failed = 42 - x
Finally, we can equate the total score of all the students to the sum of the total scores of students who passed and students who failed:
Total score of all students = Total score of students who passed + Total score of students who failed
Substituting the values we know:
75.5 × 42 = 81x + 60(42-x)
Now we can solve this equation to find the value of x, which represents the number of students who passed the test.