a total of 50 juniors and seniors were given a mathematics test.the 35 juniors attained an average score of 80 while the 15 seniors attained an average of 70.what was the averagescore for all 50 students who took the test? please explain if you can
since the average of the 35 juniors was 80, the total of their scores was 35x80 = 2800
the average of the 15 seniors was 70, so their total was 15x70 = 1050
total sum = 3850, so for the 50 students the average was 3850/50 or 77
To find the average score for all 50 students who took the test, you need to calculate the sum of the scores of all the students and divide it by the total number of students.
First, let's find the sum of scores for the juniors. We are given that there were 35 juniors with an average score of 80. To find the sum of their scores, you multiply the average score by the number of students:
Sum of scores for juniors = 35 × 80 = 2800
Next, let's find the sum of scores for the seniors. There were 15 seniors with an average score of 70. To find the sum of their scores, you multiply the average score by the number of students:
Sum of scores for seniors = 15 × 70 = 1050
Now, to find the sum of scores for all 50 students, you add the sum of scores for juniors and the sum of scores for seniors:
Total sum of scores = Sum of scores for juniors + Sum of scores for seniors
= 2800 + 1050
= 3850
Finally, to find the average score for all 50 students, you divide the total sum of scores by the total number of students:
Average score for all 50 students = Total sum of scores / Total number of students
= 3850 / 50
= 77
Therefore, the average score for all 50 students who took the test is 77.