1. **Problem:** The Sultan of Brunei noticed that the ratio of emeralds to rubies is the same as the ratio of diamonds to pearls. Given 85 emeralds, 119 rubies, and 45 diamonds, find the number of pearls. 2. **Formula and rule:** If two ratios are equal, then $ \frac{\text{emeralds}}{\text{rubies}} = \frac{\text{diamonds}}{\text{pearls}} $. 3. **Set up the equation:** $$\frac{85}{119} = \frac{45}{p}$$ where $p$ is the number of pearls. 4. **Cross multiply:** $$85 \times p = 119 \times 45$$ 5. **Calculate the right side:** $$119 \times 45 = 5355$$ 6. **Solve for $p$:** $$p = \frac{5355}{85}$$ 7. **Simplify the fraction:** $$p = \frac{\cancel{5355}}{\cancel{85}} = 63$$ 8. **Answer:** The Sultan had $63$ pearls. **Final answer: D 63**