A recipe for 4 servings requires salt and pepper to be added in the ratio of 2:3. If the recipe is adjusted from 4 to 8 serving, what is the ratio of the salt and pepper that must now be added?

Options

A. `4:3`
B. `2:6`
C. `2:3`
D. `3:2`

Answer

To solve the problem, we need to determine the ratio of salt and pepper when the recipe is adjusted from 4 servings to 8 servings.

### Step-by-Step Solution:

1. **Identify the Ratio for 4 Servings:**
The recipe states that for 4 servings, the ratio of salt to pepper is 2:3. We can express the amounts of salt and pepper in terms of a variable \( k \):
- Amount of salt = \( 2k \)
- Amount of pepper = \( 3k \)

2. **Calculate the Total Amounts for 4 Servings:**
For 4 servings, the total amounts are:
- Salt = \( 2k \)
- Pepper = \( 3k \)

3. **Determine the New Servings:**
The recipe is adjusted to 8 servings. Since 8 servings is double the 4 servings, we can conclude that the amounts of salt and pepper will also double.
- New amount of salt = \( 2 \times (2k) = 4k \)
- New amount of pepper = \( 2 \times (3k) = 6k \)

4. **Calculate the New Ratio:**
Now, we find the ratio of the new amounts of salt and pepper:
\[ \text{Ratio of Salt to Pepper} = \frac{4k}{6k} \]
Here, \( k \) cancels out:
\[ = \frac{4}{6} \]

5. **Simplify the Ratio:**
We can simplify \( \frac{4}{6} \) by dividing both the numerator and denominator by 2:
\[ = \frac{2}{3} \]

6. **Final Answer:**
Therefore, the ratio of salt to pepper for 8 servings is \( 2:3 \).