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.