The problem is (X+Y+Z)/3=82 (1).
(X+Y)/2=86 (2)
(Y+Z)/2=77 (3)
X+Y= 172 is obtained from (2)
X+Y+Z=246 from ( 1)
The solution is Z=74.
Substitute Y+Z= 154 in (3) into z to get Y=80 X=92, that is, the average score of Chinese is 92 and that of English is 74.