1. 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?
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By: anil on 05 May 2019 02.31 am
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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