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?
The mean above 70 is 81, the mean of the students below is 60.
Let nf be the number of students that failed.
sumfaildgrades+sumpassedgrades=total sum grades.
nf*60+(42-nf)81=42(75.5)
check that. solve for nf.
To find the number of students who passed the test, we can use the given information about the mean scores of the students.
Let's start by calculating the total score of all 42 students. We know that the mean (average) score of the 42 students is 75.5. Since the mean is calculated by dividing the total sum of scores by the number of students, we can multiply the mean score by the number of students to find the total sum of scores. So, 75.5 multiplied by 42 gives us the total score.
Total score of 42 students = 75.5 * 42 = 3171
Now, we also know the mean score of the students who passed the test is 81. Since we want to find the number of students who passed, we need to find the total score of the students who passed the test.
Let's assume the number of students who passed the test is x. The total score of these x students will be x multiplied by the mean score of 81.
Total score of students who passed = x * 81
Similarly, the total score of the students who failed the test can be calculated using their mean score of 60. Let's assume the number of students who failed is y.
Total score of students who failed = y * 60
Since the total sum of scores is equal to the sum of the scores of students who passed and students who failed, we can set up the equation:
Total score of 42 students = Total score of students who passed + Total score of students who failed
3171 = x * 81 + y * 60
Now, we know that the passing score is 70. So, we can set up another equation using x (number of students who passed) and y (number of students who failed):
x + y = 42 (the total number of students)
We have two equations:
3171 = x * 81 + y * 60
x + y = 42
Using these two equations, we can solve for x (number of students who passed) and y (number of students who failed).
By solving the equations, we find that x = 30 and y = 12.
Therefore, 30 students passed the test.