The average (arithmetic mean) of all scores on a certain algebra test was 90. If the average of the 8 male students’ grades was 82, and the average of the female students’ grades was 92, how many female students took the test? Choose the correct choice
A) 8  B) 9  C) 10  D) 21  E) 32
Total Marks of male = M   Total Marks of female = F   Number of males = 8   Number of females = f   Given: (M+F)/(8+f) = 90 -------------1   Also given, M/8 = 82 Thus M = 656 ---------2   Also, F/f = 92 thus F = 92 F - --------3   Put 2 and 3 in 1: we get   (656+92f)/(8+f) = 90   solving this we get f = 32   Ans: 32
<result>E</result>
The average (arithmetic mean) of all scores on a certain algebra test was 90. If the average of the 8 male students’ grades was 82, and the average of the female students’ grades was 92, how many female students took the test?