1. **State the problem:** Josie wants to make lemonade servings using the recipe amounts: syrup 3/4 oz, lemon juice 2 1/4 oz, and water 5 oz per serving. She has 20 oz syrup, 33 oz lemon juice, and 1/2 gallon water. We need to find how many servings she can make. 2. **Convert all amounts to the same units:** 1 gallon = 128 oz, so 1/2 gallon = $\frac{1}{2} \times 128 = 64$ oz water. 3. **Write the formula for servings:** Number of servings = minimum of (available ingredient amount) divided by (amount per serving). 4. **Calculate servings for each ingredient:** - Syrup servings: $\frac{20}{\frac{3}{4}} = 20 \times \frac{4}{3} = \frac{80}{3} \approx 26.67$ - Lemon juice servings: $\frac{33}{2 \frac{1}{4}} = \frac{33}{\frac{9}{4}} = 33 \times \frac{4}{9} = \frac{132}{9} \approx 14.67$ - Water servings: $\frac{64}{5} = 12.8$ 5. **Determine the limiting ingredient:** The smallest number of servings is water with 12.8 servings. 6. **Final answer:** Josie can make **12 servings** of lemonade (rounding down to whole servings).