1. **State the problem:** Josie wants to make lemonade servings using syrup, lemon juice, and water. Each serving requires 3/4 ounces of syrup, 2 1/4 ounces of lemon juice, and 5 ounces of water. Josie has 20 ounces of syrup, 33 ounces of lemon juice, and 1/2 gallon of water. We need to find how many servings Josie can make. 2. **Convert all amounts to the same units:** 1/2 gallon of water equals 64 ounces (since 1 gallon = 128 ounces). 3. **Write the formula:** The number of servings Josie can make is limited by the ingredient that runs out first. Calculate servings for each ingredient: $$\text{servings} = \frac{\text{available amount}}{\text{amount per serving}}$$ 4. **Calculate servings for each ingredient:** - Syrup: $$\frac{20}{\frac{3}{4}} = 20 \times \frac{4}{3} = \frac{80}{3} \approx 26.67$$ - Lemon juice: Convert 2 1/4 to improper fraction: $$2 \frac{1}{4} = \frac{9}{4}$$ $$\frac{33}{\frac{9}{4}} = 33 \times \frac{4}{9} = \frac{132}{9} \approx 14.67$$ - Water: $$\frac{64}{5} = 12.8$$ 5. **Determine the limiting ingredient:** The smallest number of servings is 12.8 (water), so Josie can make 12 full servings (since partial servings are not complete). **Final answer:** Josie can make **12 servings** of lemonade.