Three maths classes: A, B and C take an algebra test. The average score of class A is 83. The average score of class B is 76. The average score of class C is 85. The average score of class A and B is 79 and average score of class B and C is 81. What is the average score of classes A, B, C ? Choose the most appropriate option:  A) 81.8  B) 81.1  C) 81.2  D) 81.5  E) 81.9
Let the number of students in classes A, B and C be P, Q and R respectively.   Then, total score of A = 83P, total score of B = 76Q, total score of C = 85R.   Also given that,   (83P + 76Q) / (P + Q) = 79   =&gt;4P = 3Q.   (76Q + 85R)/(Q + R) = 81   =&gt;4R = 5Q,   =&gt;Q = 4P/3 and R = 5P/3   Therefore, average score of A, B, C = ( 83P + 76Q + 85R ) / (P + Q + R) = 978/12= 
<gadget id="calculator">978/12</gadget>
<output>163/2 = around 81.5</output>
81.5   Answer: 81.5
<result>D</result>
Three maths classes: A, B and C take an algebra test. The average score of class A is 83. The average score of class B is 76. The average score of class C is 85. The average score of class A and B is 79 and average score of class B and C is 81. What is the average score of classes A, B, C ?