To determine which sets of ingredients are in a proportional relationship with the given recipe, we need to compare the ratios of the ingredients to the given ratio of 12 parts oil, 3 parts vinegar, and 2 parts honey.
For example, if we take the first set of ingredients: 16 parts oil, 4 parts vinegar, and 2 parts honey, we can calculate the ratios:
Oil: 16 parts / 4 = 4 parts
Vinegar: 4 parts / 4 = 1 part
Honey: 2 parts / 4 = 0.5 parts
Comparing these ratios to the original recipe, we can see that they are proportional, as each ratio is a multiple of the original ratio:
Oil: 4 / 12 = 1/3
Vinegar: 1 / 3 = 1/3
Honey: 0.5 / 2 = 1/4
Therefore, the first set of ingredients is in a proportional relationship with the recipe. We can apply the same process to the other sets of ingredients to see if they are proportional as well.