Three math classes; X, Y, and Z, take an algebra test.
The average score in class X is 83.
The average score in class Y is 76.
The average score in class Z is 85.
The average score of all students in classes X and Y together is 79.
The average score of all students in classes Y and Z together is 81.
What is the average for all three classes?
Explanation:
Let there be x number of students in class X, y number of students in class Y and z number of students in class Z.
∴ 83x + 76y = 79(x + y)
∴ 4x = 3y
Similarly,
76y + 85z = 81(y + z)
∴ 4z = 5y
∴ 20x = 15y = 12z
∴ x : y : z = 3 : 4 : 5
∴ The average of all the three classes
=83×3+76×4+85×53+4+5=81.5
Hence, option (b).
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