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?
Mean = (sum of scores)/number of scores
If I understand your problem correctly, the ratio of the three scores are 6:5:3 and the mean of the three = 75. If that is what you are saying, then:
75 = (6x + 5x + 3x)/3 = 14x/3
14x = 225
Solve for x.
However, this does not give you the answers you indicate. Sorry. Can you state the problem more clearly?
To find out how many points the three students had, we can set up a system of equations and solve them.
Let's represent the initial total points of all the students before relocation as T. Since there are no specific values given, we can work with variables.
According to the given information, the average before relocation was 74 points, so the initial sum of points would be 74 times the total number of students, which we can represent as:
T = 74 * (number of students)
After three students relocate, the total number of students is reduced by three. We can represent this as:
(number of students - 3) = (6 + 5 + 3)
Simplifying the equation above, we get:
(number of students - 3) = 14
Now let's use this equation to find the value of "number of students":
number of students = 14 + 3
number of students = 17
Now that we know the total number of students, we can calculate the total points after relocation using the average of 75 points:
T = 75 * (number of students)
T = 75 * 17
T = 1275
So, the initial total points before relocation were 1275. Now let's find out how many points the three students had.
We know the ratio of points for the three students was 6:5:3. Let's assign variables to their points as follows:
Student 1: 6x
Student 2: 5x
Student 3: 3x
The sum of their points would be:
6x + 5x + 3x = 1275
14x = 1275
x = 1275 / 14
x ≈ 91.071
Now, let's calculate their individual scores:
Student 1: 6x ≈ 6 * 91.071 ≈ 546.43 (approximately 546.43 points)
Student 2: 5x ≈ 5 * 91.071 ≈ 455.355 (approximately 455.355 points)
Student 3: 3x ≈ 3 * 91.071 ≈ 273.213 (approximately 273.213 points)
So, the three students had approximately 546.43, 455.355, and 273.213 points, respectively. These values can be rounded to the nearest whole number, resulting in 546, 455, and 273 points.