Answer:
To solve this, we need to determine the total number of cups of juice needed for 20 servings according to the recipe.
If 6 servings require 2 cups of juice, then 1 serving requires \( \frac{2}{6} \) cups of juice.
So, for 20 servings:
\[ \text{Total cups of juice needed} = \text{1 serving juice requirement} \times \text{number of servings} \]
\[ = \left( \frac{2}{6} \right) \times 20 \]
\[ = \frac{2 \times 20}{6} \]
\[ = \frac{40}{6} \]
\[ = 6\frac{2}{6} \]
\[ = 6.67 \]
Since we can't have a fraction of a cup for juice in this context, we would round up to the nearest whole number.
So, the total number of cups of juice needed for 20 servings is 7.
Therefore, the correct answer is not provided in the options given.
Step-by-step explanation:
1. **Determine the juice requirement per serving:** According to the recipe, 6 servings require 2 cups of juice. So, to find out how much juice is needed per serving, we divide the total juice by the number of servings: \( \frac{2}{6} \) cups per serving.
2. **Calculate the total juice needed for 20 servings:** Now that we know how much juice is needed per serving, we multiply this amount by the number of servings required. So, \( \frac{2}{6} \) cups per serving multiplied by 20 servings equals \( \frac{2}{6} \times 20 \).
3. **Simplify the expression:** \( \frac{2}{6} \times 20 \) simplifies to \( \frac{40}{6} \).
4. **Convert the result to a mixed fraction:** \( \frac{40}{6} \) is equivalent to \( 6\frac{2}{6} \).
5. **Round the result:** Since we can't have a fraction of a cup in this context, we round up to the nearest whole number. \( 6\frac{2}{6} \) is approximately 7.
6. **Conclusion:** The total number of cups of juice needed for 20 servings is 7. However, none of the options provided match this result, suggesting there may be a mistake in the problem or the options.
