1. **Stating the problem:** We have two recipes, one using imperial US measurements and one using metric measurements. Each recipe yields between 8-12 portions and has at least 6 ingredients. We need to scale each recipe up to 16 servings and down to 6 servings, showing the scale factor (SF) each time. 2. **Original Recipes:** **Recipe 1 (Imperial US): Pancakes** - Flour: 2 cups - Milk: 1.5 cups - Eggs: 2 large - Sugar: 2 tablespoons - Baking powder: 2 teaspoons - Salt: 0.5 teaspoon - Butter (melted): 2 tablespoons - Yield: 10 servings **Recipe 2 (Metric): Fruit Salad** - Apples: 500 grams - Bananas: 300 grams - Oranges: 400 grams - Grapes: 200 grams - Honey: 50 grams - Lemon juice: 30 milliliters - Mint leaves: 10 grams - Yield: 10 servings 3. **Formula for scaling recipes:** $$\text{Scaled amount} = \text{Original amount} \times \text{Scale Factor (SF)}$$ Where $$\text{SF} = \frac{\text{Desired servings}}{\text{Original servings}}$$ 4. **Scaling Pancakes recipe:** - Original servings = 10 **Scale Up to 16 servings:** $$SF = \frac{16}{10} = 1.6$$ Multiply each ingredient by 1.6. **Scale Down to 6 servings:** $$SF = \frac{6}{10} = 0.6$$ Multiply each ingredient by 0.6. 5. **Scaled Pancakes ingredients:** - Flour: $2 \times 1.6 = 3.2$ cups (up), $2 \times 0.6 = 1.2$ cups (down) - Milk: $1.5 \times 1.6 = 2.4$ cups (up), $1.5 \times 0.6 = 0.9$ cups (down) - Eggs: $2 \times 1.6 = 3.2$ eggs (up), $2 \times 0.6 = 1.2$ eggs (down) - Sugar: $2 \times 1.6 = 3.2$ tbsp (up), $2 \times 0.6 = 1.2$ tbsp (down) - Baking powder: $2 \times 1.6 = 3.2$ tsp (up), $2 \times 0.6 = 1.2$ tsp (down) - Salt: $0.5 \times 1.6 = 0.8$ tsp (up), $0.5 \times 0.6 = 0.3$ tsp (down) - Butter: $2 \times 1.6 = 3.2$ tbsp (up), $2 \times 0.6 = 1.2$ tbsp (down) 6. **Scaling Fruit Salad recipe:** - Original servings = 10 **Scale Up to 16 servings:** $$SF = \frac{16}{10} = 1.6$$ **Scale Down to 6 servings:** $$SF = \frac{6}{10} = 0.6$$ 7. **Scaled Fruit Salad ingredients:** - Apples: $500 \times 1.6 = 800$ g (up), $500 \times 0.6 = 300$ g (down) - Bananas: $300 \times 1.6 = 480$ g (up), $300 \times 0.6 = 180$ g (down) - Oranges: $400 \times 1.6 = 640$ g (up), $400 \times 0.6 = 240$ g (down) - Grapes: $200 \times 1.6 = 320$ g (up), $200 \times 0.6 = 120$ g (down) - Honey: $50 \times 1.6 = 80$ g (up), $50 \times 0.6 = 30$ g (down) - Lemon juice: $30 \times 1.6 = 48$ ml (up), $30 \times 0.6 = 18$ ml (down) - Mint leaves: $10 \times 1.6 = 16$ g (up), $10 \times 0.6 = 6$ g (down) **Final answers:** - Pancakes scaled to 16 servings and 6 servings with SF 1.6 and 0.6 respectively. - Fruit Salad scaled to 16 servings and 6 servings with SF 1.6 and 0.6 respectively.