A salad dressing recipe uses 9 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. 18 tbsp oil, 6 tbsp vinegar, 4 tbsp honey
B. 6 tbsp oil, 2.5 tbsp vinegar, 1 tbsp honey
C. 4.5 tbsp oil, 1.5 tbsp vinegar, 1 tbsp honey
D. 12 tbsp oil, 4.5 tbsp vinegar, 3 tbsp honey
E. 24 tbsp oil, 6.5 tbsp vinegar, 5.5 tbsp honey

By comparing the ratios of each set of ingredients to the original recipe ratio of 9:3:2 (oil:vinegar:honey), we see that only option a) 18 tbsp oil, 6 tbsp vinegar, 4 tbsp honey is in a proportional relationship with the original recipe.

Explanation:

To determine which sets are in a proportional relationship with the original recipe, we can set up ratios since the recipe is given in parts. The original recipe can be seen as a ratio of 9:3:2 (oil:vinegar:honey). Let's compare this ratio with the sets given in the options.

a) 18:6:4 – This option is the same as the original ratio. If we divide each number by 2, we get back to 9:3:2.

b) 6:2.5:1 – If we try to divide to get the original ratio, it does not work. So this is not proportional.c) 4.5:1.5:1 – Divide each by 1.5 and we get 3:1:⅔. It's not the same as the original ratio, so it isn't proportional.d) 12:4.5:3 – Dividing each by 3, we get 4:1.5:1, which is not proportional to the original ratio.e) 24:6.5:5.5 – There's no common divisor to reach the original ratio, so it's not proportional.

Therefore, the only set of ingredients that are in a proportional relationship with the original recipe is option a) 18 tbsp oil, 6 tbsp vinegar, 4 tbsp honey.

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