Three science classes A, B and C take a Life Science 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 CG is 81. Then the average score of classes A, B and C is.

Given that average score of class A is 83. Let's consider number of students in class A as "x"

=> $$\frac{sum of scores of class A}{x}$$ = 83

=> sum of scores of class A = 83x

Given that average score of class B is 76. Let's consider number of students in class B as "y"

=> $$\frac{sum of scores of class B}{y}$$ = 76

=> sum of scores of class B = 76y

Given that average score of class C is 85. Let's consider number of students in class C as "z"

=> $$\frac{sum of scores of class C}{z}$$ = 85

=> sum of scores of class C = 85z

Similarly from other given statements,

$$\frac{sum of scores of classes A,B}{x+y}$$ =79

=> $$\frac{83x+76y}{x+y}$$=79

=> 83x+76y=79x+79y

=> 4x=3y => x=$$\frac{3y}{4}$$

and $$\frac{sum of scores of classes B,C}{y+z}$$ =81

=> $$\frac{76y+85z}{y+z}$$ = 81

=> 76y+85z=81y+81z

=> 4z=5y => z=$$\frac{5y}{4}$$

Therefore, average score of classes A,B & C is 

$$\frac{83x+76y+85z}{x+y+z}$$= $$\frac{83(\frac{3y}{4})+76y+85(\frac{5y}{4})}{\frac{3y}{4}+y+\frac{5y}{4}}$$=$$\frac{978}{12}$$=81.5