Solving a word problem involving age relationships between Katlyn and Sarah using algebra.

- Let $x$ be Katlyn's current age.
- Then Sarah's current age is $2x - 36$.
- In 6 years, Katlyn will be $x + 6$ and Sarah will be $(2x - 36) + 6 = 2x - 30$.
- According to the problem, in 6 years, Sarah’s age will be 12 years more than half of Katlyn’s age: $2x - 30 = \frac{1}{2}(x + 6) + 12$.
- Solve the equation:
- Multiply both sides by 2: $4x - 60 = x + 6 + 24$.
- Simplify: $4x - 60 = x + 30$.
- Subtract $x$ from both sides: $3x - 60 = 30$.
- Add 60 to both sides: $3x = 90$.
- Divide by 3: $x = 30$.
- Katlyn is 30 years old.
- Sarah is $2(30) - 36 = 60 - 36 = 24$ years old.