At Jefferson School, both 6th grade and 7th grade classes took a math test. The average score for the 6th grade is 80 and for the 7th grade is 90. If there are twice as many students in the 7th grade as that in the 6th grade, what is the average test score for both grades together?
Suppose we let
x = # 6th graders
Then 2x = # 7th graders
Now find the average of all the students:
(80x + 90*2x)/(x+2x) = (80x+180x)/3x = 260/3 = 86.6
Just FYI, note that since 2/3 of the students are 7th graders, the total average is 2/3 of the way from 80 to 90.
To find the average test score for both grades together, we need to calculate the total score for both grades and then divide it by the total number of students.
Let's assume there are 'x' students in the 6th grade. Since there are twice as many students in the 7th grade, the number of students in the 7th grade would be 2x.
The average score for the 6th grade is 80, so the total score for the 6th grade would be 80 * x.
Similarly, the average score for the 7th grade is 90, so the total score for the 7th grade would be 90 * 2x.
The total score for both grades would be (80 * x) + (90 * 2x).
The total number of students in both grades would be x + 2x.
To find the average test score, we divide the total score by the total number of students:
(80 * x + 90 * 2x) / (x + 2x)
Simplifying the expression:
(80x + 180x) / 3x
260x / 3x
The 'x' terms cancel out, and we are left with:
260 / 3
Therefore, the average test score for both grades together is 260/3.
To find the average test score for both grades together, we need to consider the total number of students and their respective average scores.
Let's assume there are x students in the 6th grade. Since we know that there are twice as many students in the 7th grade, that means there are 2x students in the 7th grade.
To calculate the average test score for both grades, we need to find the sum of the individual grade scores and divide it by the total number of students.
For the 6th grade:
Total score for 6th grade = Average score * Number of students
Total score for 6th grade = 80 * x
For the 7th grade:
Total score for 7th grade = Average score * Number of students
Total score for 7th grade = 90 * 2x
To find the average test score for both grades, we need to sum up the total scores for each grade and divide it by the total number of students.
Total score for both grades = Total score for 6th grade + Total score for 7th grade
Total score for both grades = (80 * x) + (90 * 2x)
Total number of students = Number of students in 6th grade + Number of students in 7th grade
Total number of students = x + 2x
Now we can calculate the average test score for both grades together:
Average test score for both grades = Total score for both grades / Total number of students
Average test score for both grades = [(80 * x) + (90 * 2x)] / (x + 2x)
Simplifying the expression further:
Average test score for both grades = (80x + 180x) / 3x
Average test score for both grades = (260x) / (3x)
Average test score for both grades = 260 / 3
Average test score for both grades ≈ 86.67
Therefore, the average test score for both grades together is approximately 86.67.