The average score for a class of 30 students was 75. The 20 male students in the class averaged 70. The female students in the class averaged:
A)75.
B)85.
C)65.
D)70.
E)80.

Question

Quizplus · Accepted Answer

Let the sum of all scores be S. Then we know that:

S/30 = 75   (average score for the whole class)

S/20 = 70   (average score for the male students)

Multiplying the second equation by 20 gives us:

S = 1400   (sum of all scores for the male students)

Now we can use this information to find the average score for the female students. Let F be the sum of all scores for the female students. Then:

(F + 1400)/30 = 75   (average score for the whole class)

(F + 1400)/10 = 75   (simplifying the left side)

F + 1400 = 750   (multiplying both sides by 10)

F = 350   (subtracting 1400 from both sides)

So the sum of all scores for the female students is 350. Since there are 10 female students, the average score for the female students is:

350/10 = 35   (average score for the female students)

Therefore, the answer is B) 85.

The Average Score for a Class of 30 Students Was