a group of 100 students took a quiz. Their average score was 76 points. If the average score for boys was 80 points and the average score for girls was 70 points, how many girls participated in the quiz
To find out how many girls participated in the quiz, we need to use the concept of weighted averages.
Let's assume there were x girls in the group. Since the average score for girls was 70, we can multiply the number of girls (x) by 70 to get the total score for the girls.
Similarly, since there were 100 students in total, the number of boys would be 100 - x. Multiplying this by their average score of 80 will give us the total score for the boys.
To find the average score for the entire group, we need to sum up the total scores for both boys and girls and divide by the total number of students.
The equation for the average score can be written as:
(70x + 80(100 - x)) / 100 = 76
Simplifying the equation:
70x + 8000 - 80x = 7600
Combining like terms:
8000 - 7600 = 80x - 70x
400 = 10x
Dividing both sides by 10:
x = 40
Therefore, there were 40 girls who participated in the quiz.