Question : Three Science classes A, B, and C take a Life Science test. The average score for class A is 83. The average score for class B is 76. The average score in class C is 85. The average score of classes A and B is 79, and the average score of classes B and C is 81. Then the average score of classes A, B, and C is:
Option 1: 81.5
Option 2: 81
Option 3: 80.5
Option 4: 80
Correct Answer: 81.5
Solution :
The average score of classes A, B, and C are 83, 76, and 85 respectively.
The average score of class A and class B = 79
The average score of class B and class C = 81
Let the number of students in classes A, B, and C be x, y, and z, respectively.
So, the total score of classes A, B, and C =
Also, total score of class (A + B) is
and total score of class (B + C) is
Now,
⇒
⇒
And,
⇒
⇒
So,
Hence, the correct answer is 81.5.
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