Let a be Alice's age, b be Barbara's age, and c be Carol's age. We have 3 given equations:

- a = b - 3
- b = c - 5
- a + b + c = 68

c = b + 5

Now plug in (1) and (2) revised into (3). We want to isolate for b.

a + b + c = 68

(b - 3) + b + (b + 5) = 68

Combine like terms:

(b + b + b) + (5 - 3) = 68

3b + 2 = 68

Run this through our equation calculator, and we get b =

**22**