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?

Question

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.