Question

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?
(1) 81 (2) 81.5 (3) 82 (4) 84.5

Answer 1

No fo student in class X = x

Total score of student in Class X = 83x

No of students in Class Y= y

Total score of student in Class Y = 76y

No of students in Class Z = z

Total score of students in Class Z = 85z

Average score of class X and Y = 79

   83x   +   76y    = 79

        x + y

83x + 76y = 79(x + y)

83x - 79x = 79y - 76y

4x = 3y

x = 3y/4

Similarly we we should with classes Y and Z

76y + 85z = 81y + 81z

z = 5y/4

Average of three classes =

   83x + 76y + 85z    =     83 (3y/4) + 76y  +  85 (5y/4)  

       x + y + z                               (3y/4) + y + (5y/4)

249/4 + 304/4  +  425/4    = 249 + 304 + 425  = 978 / 12 = 81.50

  3/4 + 4y/4 + 5/4                                    12