In a test, the average was 74 points/100 points. After the test, three of students relocate. Then the average was 75 points/100. The circumstances of the students were 6:5:3. How many points did the three students have?
I know the answere is 45, 75 and 90, but can you write the operation?
To find the total number of points earned by the three students, we need to calculate the total points earned by all the students before and after relocation, and then find the difference between the two totals.
Let's break down the problem step by step:
Step 1: Calculate the total points earned by all the students before relocation.
If the average was 74 points with 6:5:3 circumstances, that means there were 6 + 5 + 3 = 14 students in total.
Multiplying the average score (74) by the number of students (14), we get: 74 * 14 = 1036 points.
Step 2: Calculate the total points earned by all the students after relocation.
Given that the average became 75 points with the same circumstances (6:5:3), the number of students remains the same (14).
Again, multiplying the average score (75) by the number of students (14), we get: 75 * 14 = 1050 points.
Step 3: Find the difference between the two totals to determine the points earned by the three students who relocated.
To find the points earned by the three students who relocated, we subtract the total points earned by all the students before relocation from the total points earned by all the students after relocation: 1050 - 1036 = 14 points.
The circumstances of the relocated students were 6:5:3, which represents a total of 14 students. Since they collectively earned 14 points, we can divide these points among these students based on the given ratio: 6 points for the first student, 5 points for the second student, and 3 points for the third student.
Therefore, the three students earned 6, 5, and 3 points each, respectively.