A group of 100 Students took a quiz.

Question

Thier avg was 76 points.  Boys avg was 80.  Girls avg. was 70. How many girls took the quiz

Answer 1

1. B+G=100 (choose variables, B for number of boys, G for number of girls)
2. (80B+70G)/100 = 76 (definition of average...and remember, if the boys' average was 80, we can pretend that every boy scored exactly 80)
3. 80B+70G=7600 (simplification)
4. 8B+7G=760 (divide by 10)
5. B=100-G (solve equation 1 for one of the variables)
6. 8(100-G)+7G=760 (substitute equation from step 5 into equation from step 4)
7. 800-8G+7G=760 (distribution)
8. 40=G (solve for G)
9. B=100-G=100-40=60

 

Therefore you have 40 girls and 60 boys