1. **State the problem:** Zoey wants to make 10 servings of trail mix. The original recipe makes 5 servings and calls for 1 3/4 cups of almonds. We need to find how many cups of almonds Zoey needs for 10 servings. 2. **Formula:** To find the amount needed for more servings, use the proportion: $$\text{Amount for new servings} = \text{Original amount} \times \frac{\text{New servings}}{\text{Original servings}}$$ 3. **Convert mixed number to improper fraction:** $$1\ \frac{3}{4} = \frac{4 \times 1 + 3}{4} = \frac{7}{4}$$ 4. **Apply the formula:** $$\text{Almonds needed} = \frac{7}{4} \times \frac{10}{5}$$ 5. **Simplify the fraction:** $$\frac{7}{4} \times \frac{10}{5} = \frac{7}{4} \times \cancel{\frac{10}{5}}^{\cancel{2}} = \frac{7}{4} \times 2 = \frac{7 \times 2}{4} = \frac{14}{4}$$ 6. **Simplify the fraction further:** $$\frac{14}{4} = \frac{\cancel{14}^{7}}{\cancel{4}^{2}} = \frac{7}{2}$$ 7. **Convert back to mixed number:** $$\frac{7}{2} = 3\ \frac{1}{2}$$ **Final answer:** Zoey needs 3 1/2 cups of almonds to make 10 servings.