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Three 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 the three classes?
Let x , y and z be no. of students in class X, Y ,Z respectively.
From 1st condition we have
83*x+76*y = 79*x+79*y which give 4x = 3y.
Next we have 76*y + 85*z = 81(y+z) which give 4z = 5y .
Now overall average of all the classes can be given as $$\frac{83x+76y+85z}{x+y+z}$$
Substitute the relations in above equation we get,
$$\frac{83x+76y+85z}{x+y+z}$$ = (83*3/4 + 76 + 85*5/4)/(3/4 + 1 + 5/4) = 978/12 = 81.5
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