Five years ago Hank was half his sister's age at that time. Right now the sum of

their ages is 43. How old will they both be next year?

Hank: 17 Sister: 28

Step-by-step explanation:

Five years ago the sum of their ages was 10 less than it is now, so was 33. If Hank was half his sister's age, his age was 1/3 of this total. 5 years ago, Hank was 11 and his sister was 22.

Next year, both will be 6 years older than those ages, so ...

Hank will be 17

Hank's sister will be 28