To determine which measurements result in a dressing that is sweeter than the original recipe, we need to analyze the ratio of sugar to vinegar in each of the options compared to the original recipe.
The original recipe has the following ratios of sugar (S) to vinegar (V) based on the amounts given:
-
For 12 tbsp vinegar and 8 tbsp sugar: \[ \text{Ratio} = \frac{S}{V} = \frac{8}{12} = \frac{2}{3} \approx 0.67 \]
-
For 18 tbsp vinegar and 12 tbsp sugar: \[ \text{Ratio} = \frac{12}{18} = \frac{2}{3} \approx 0.67 \]
-
For 24 tbsp vinegar and 16 tbsp sugar: \[ \text{Ratio} = \frac{16}{24} = \frac{2}{3} \approx 0.67 \]
In all cases, the ratio of sugar to vinegar from the original recipe is \( \frac{2}{3} \).
Now, let's analyze each option:
A. 3 tbsp vinegar, 2 tbsp sugar \[ \text{Ratio} = \frac{2}{3} \approx 0.67 \]
B. 8 tbsp vinegar, 6 tbsp sugar \[ \text{Ratio} = \frac{6}{8} = \frac{3}{4} = 0.75 \] (Sweeter than the original)
C. 16 tbsp vinegar, 8 tbsp sugar \[ \text{Ratio} = \frac{8}{16} = \frac{1}{2} = 0.5 \] (Not sweeter than the original)
D. 24 tbsp vinegar, 3 tbsp sugar \[ \text{Ratio} = \frac{3}{24} = \frac{1}{8} = 0.125 \] (Not sweeter than the original)
Based on this analysis, the only option that results in a dressing that is sweeter than the original recipe is:
B. 8 tbsp vinegar, 6 tbsp sugar.