1. **State the problem:** We are given the ratio of goals scored by Arjun, Simon, and Kath as $2:5:8$. Simon scored 12 more goals than Arjun. We need to find how many goals Kath scored. 2. **Set variables:** Let the common multiplier for the ratio be $x$. Then: - Arjun's goals = $2x$ - Simon's goals = $5x$ - Kath's goals = $8x$ 3. **Use the given information:** Simon scored 12 more goals than Arjun, so: $$5x - 2x = 12$$ 4. **Simplify the equation:** $$3x = 12$$ 5. **Solve for $x$:** $$x = \frac{12}{3} = 4$$ 6. **Find Kath's goals:** $$8x = 8 \times 4 = 32$$ **Final answer:** Kath scored 32 goals.