A salad dressing recipe uses 12 parts oil, 3 parts vinegar, and 2 parts honey. Which of the following sets of ingredients are in a proportional relationship with the recipe? Select all that apply.

A. 9 Tbsp oil, 2 Tbsp vinegar, 1.5 Tbsp honey
B. 6 Tbsp oil, 1.5 Tbsp vinegar, 1 Tbsp honey
C. 15 Tbsp oil, 4 Tbsp vinegar, 3 Tbsp honey
D. 18 Tbsp oil, 4.5 Tbsp vinegar, 3 Tbsp honey
E. 24 Tbsp oil, 6 Tbsp vinegar, 4 Tbsp honey

The sets of ingredients that are in a proportional relationship with the original salad dressing recipe are the ones with 6 Tbsp oil, 1.5 Tbsp vinegar, 1 Tbsp honey; 18 Tbsp oil, 4.5 Tbsp vinegar, 3 Tbsp honey; and 24 Tbsp oil, 6 Tbsp vinegar, 4 Tbsp honey.

Explanation:

To determine which sets of ingredients are in a proportional relationship with the original recipe that uses 12 parts oil, 3 parts vinegar, and 2 parts honey, we need to check if the ratios between the amounts of oil, vinegar, and honey in each set are the same as the ratios in the recipe.

Recipe Ratio: 12 parts oil : 3 parts vinegar : 2 parts honey, which simplifies to 4 : 1 : 2/3.

Let's examine each set:

9 Tbsp oil, 2 Tbsp vinegar, 1.5 Tbsp honey: This simplifies to a ratio of 4.5 : 1 : 0.75, which is not the same ratio as the recipe.
6 Tbsp oil, 1.5 Tbsp vinegar, 1 Tbsp honey: This set can be simplified to a ratio of 4 : 1 : 2/3, which matches the recipe ratio.
15 Tbsp oil, 4 Tbsp vinegar, 3 Tbsp honey: The ratio is 3.75 : 1 : 0.75, which does not match the recipe ratio.
18 Tbsp oil, 4.5 Tbsp vinegar, 3 Tbsp honey: This set also simplifies to the ratio of 4 : 1 : 2/3, matching the recipe ratio.
24 Tbsp oil, 6 Tbsp vinegar, 4 Tbsp honey: This equates to a ratio of 4 : 1 : 2/3, which is in accordance with the recipe ratio.

Therefore, the sets of ingredients that are in a proportional relationship with the recipe are:

6 Tbsp oil, 1.5 Tbsp vinegar, 1 Tbsp honey
18 Tbsp oil, 4.5 Tbsp vinegar, 3 Tbsp honey
24 Tbsp oil, 6 Tbsp vinegar, 4 Tbsp honey