Question

Three science classes A, B and C take a life science test. The average score of a class A is $83$. The average score of a class B is $76$. The average score of a class C is $85$. The average score of a class A and B is $79$ and average score of a class B and C is $81$. Then the average score of classes A,B and C is

Answer 1

Avg$\left(A\right)=83=\frac{TotalscoreofA}{TotalstudentsinA}$

Avg$(A+B)=76=$$\frac{Totalscoreof(A+B)}{Totalstudentsin(A+B)}$

$⟹83\times$ total students in $A$$+73\times$ total students in$B$$=76\times$ total students in $A$$+76\times$ total students in $B$

$⟹$ total students in $A=\frac{3}{4}\times$Total students in $B$

Avg$(B+C)=81$

Following previous methods,

Total students in $C=$$\frac{5}{4}\times$Total students in $B$

Total score$=$Total score of $A+$Total score of $B+$Total score of $C$

$=\frac{3}{4}\times$Total students in $B$+ $76\times$ total students in $B$$+\frac{5}{4}\times$Total students in $B$

$(\frac{249}{4}+76+\frac{415}{4})\times$ total students in $B$

Total students$=$Total students in $A+$Total students in $B+$Total students in $C$

$=\frac{3}{4}\times$Total students in $B$+ $76\times$ total students in $B$$+\frac{5}{4}\times$Total students in $B$$=3\times$ total students in $B$

Avg$(A+B+C)=\frac{Totalscore}{Totalstudents}$$-\frac{(\frac{249}{4}+76+\frac{415}{4})}{3}=80.66\approx 81$