Alice is 3 years younger than Barbara, and Barbara is 5 years younger than Carol. Together the siste

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Alice is 3 years younger than Barbara, and Barbara is 5 years younger than Carol. Together the sisters are 68 years old. How old is Barbara?

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

1. a = b - 3
2. b = c - 5
3. a + b + c = 68

Rearrange (2)
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