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 score for all the three classes, taken together?  Pick one:	A) 81	B) 81.5	C) 82	D) 84.5	E) None of these
Explanation :   Let the number of students in classes X, Y and Z be a,   b and c respectively. Then   Total of X = 83a   Total of Y = 76b   Total of Z = 85c   And , (83a + 76b) / (a + b) = 79. i.e 4a = 3b.   Also, (76b + 85c) / (b + c) = 81. i.e 4c = 5b.   Hence, b= (4/3)a, c =(5/4)b = (5/4) x (4/3)a = (5/3)a.   Average of X, Y and Z = (83a + 76b + 85c ) / (a + b + c).   =&gt; 83a+76∗(4/3)a+85∗(5/3)a /a+(4/3)a+(5/3)a .   =&gt; 978/12= 
<gadget id="calculator">978/12</gadget>
<output>163/2 = around 81.5</output>
&gt; 81.5   Answer : 81.5
<result>B</result>
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 score for all the three classes, taken together?