10.Thirty students in a chemistry class took a test on which the overall average score was 78. If the average score for 15 of those students was 85, what was the average score for the remaining members of the class?
I know that "average" means dividing, but i'm not sure what to do.
78*30 = 2340 total score
85 * 15 = 1275 score for top 15 students
2340 - 1275 = 1065
1065 / 15 = ?
71
Yes.
To find the average score for the remaining members of the class, you need to first find the total score of all the students. Then, you can subtract the total score of the 15 students whose average score is known. Finally, you divide the remaining total score by the number of remaining students.
Here's how you can solve it step by step:
1. Multiply the average score (78) by the total number of students (30) to find the total score for all the students.
Total score = Average score * Number of students
Total score = 78 * 30
Total score = 2340
2. Multiply the average score of the known 15 students (85) by the number of those students to find the total score for the known students.
Total score of known students = Average score of known students * Number of known students
Total score of known students = 85 * 15
Total score of known students = 1275
3. Subtract the total score of the known students from the total score of all the students to get the total score of the remaining students.
Total score of remaining students = Total score - Total score of known students
Total score of remaining students = 2340 - 1275
Total score of remaining students = 1065
4. Finally, divide the total score of the remaining students by the number of remaining students to find their average score.
Average score of remaining students = Total score of remaining students ÷ Number of remaining students
Average score of remaining students = 1065 ÷ (30 - 15)
Average score of remaining students = 1065 ÷ 15
Average score of remaining students = 71
So, the average score for the remaining members of the class is 71.