Question

A recipe for 10 servings of raspberry sorbet calls for 2 cups of water, 1 and one-half cups of granulated sugar, and 4 cups of frozen raspberries, thawed. How many gallons of water would the recipe call for if a school made 320 servings for students to eat at lunch?
4 gallons
8 gallons
40 gallons
80 gallons

Answer 1

To determine how many gallons of water are needed for 320 servings of raspberry sorbet based on the original recipe for 10 servings, we can follow these steps:

1. **Find the scaling factor:**
The original recipe is for 10 servings. We need to find the amount needed for 320 servings.
\[
\text{Scaling Factor} = \frac{320 \text{ servings}}{10 \text{ servings}} = 32
\]

2. **Determine the amount of water needed for 320 servings:**
The original recipe calls for 2 cups of water for 10 servings. Therefore, for 320 servings:
\[
\text{Water for 320 servings} = 2 \text{ cups} \times 32 = 64 \text{ cups}
\]

3. **Convert cups to gallons:**
There are 16 cups in a gallon. To convert cups to gallons:
\[
\text{Gallons of water} = \frac{64 \text{ cups}}{16 \text{ cups per gallon}} = 4 \text{ gallons}
\]

Thus, the recipe for 320 servings would call for **4 gallons** of water.

The correct answer is **4 gallons**.