find three consecutive even integers such that one half of their sum is between 15 and 21.

Let numbers be n-1,n,n+1
Thus sum n-1+n+n+1=3n-1+1=3n
Given half of sum falls between 15 and 21
So sum's half=3n/2
implies 15<3n/2<21
Thus multiply by 2
30<n<42
We can take n from 31 to 41
3 number combinations
30,31,32
31,32,33
32,33,34
33,34,35till 40,41,42

That she received $100