Question 902920
m+n=19,
11*m+13*n=209
m=19-n
11*(19-n)+13*n=209
209-11n+13*n=209
2*n=0
n=0
m=19-n
m=19 at $11 and  n=0 at $13
check
19+0=19
11*m+13*n=209
11*19+13*0=209
209+0=209
209=209
ok

This means that all students were members and paid $11