There are X winners in the fourth grade and Y winners in the sixth grade.

Total winners =x+y+43

If you have any questions, you can know that x+43 = 7/11(x+y+43) (1).

y+43=2/3(x+y+43)+3 (2)

4x-7y+ 172 = 0 from ( 1)

Y-2x+34=0 from (2)

X=4 1 y=48。

Please accept the answer.