SOLUTION: In a class test, the average score for the girls was 83 and the average score for the boys was 71. If the average of all the students was 80, what percent of all the students were

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: In a class test, the average score for the girls was 83 and the average score for the boys was 71. If the average of all the students was 80, what percent of all the students were       Log On


   

Question 1110924: In a class test, the average score for the girls was 83 and the average score for the boys was 71. If the average of all the students was 80, what percent of all the students were girls.
Answer by ikleyn(52790) About Me  (Show Source):
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From the condition, the scores earned by all girls were 83G, where G is the number of girls.


The scores, earned by boys, were 71B, where B is the number of boys.


Also, we are given that  %2883G+%2B+71B%29%2F%28G%2BB%29 = 80,


which implies  83G + 71B = 80G + 80B,   or  3G = 9B,   or  G = 3B.


Thus among each 4 persons there is 3 girls and 1 boy.


The percentage  of girls among all students is  75%.

Solved.