Question

A caterer uses a potato salad dressing with the amounts, in tablespoons (tbsp), of vinegar and sugar shown in the table below.

Vinegar (tbsp) Sugar (tbsp)
12 8
18 12
24 16
She decides to make a dressing that is sweeter than the original recipe by increasing the ratio of sugar to vinegar.

Which measurements of ingredients would result in a dressing that is sweeter than the original?

Answer 1

To determine which measurements of ingredients would result in a dressing that is sweeter than the original, we need to calculate the sugar-to-vinegar ratio for the original measurements.

1. Original measurements from the table:
- Vinegar: 12 tbsp, Sugar: 8 tbsp
- Ratio of sugar to vinegar = Sugar ÷ Vinegar = 8 tbsp ÷ 12 tbsp = 2/3 or approximately 0.67.

Now let's analyze the other combinations in the table:

2. For the second set of measurements:
- Vinegar: 18 tbsp, Sugar: 12 tbsp
- Ratio of sugar to vinegar = 12 tbsp ÷ 18 tbsp = 2/3 or approximately 0.67.

3. For the third set of measurements:
- Vinegar: 24 tbsp, Sugar: 16 tbsp
- Ratio of sugar to vinegar = 16 tbsp ÷ 24 tbsp = 2/3 or approximately 0.67.

All the original measurements provided have a sugar-to-vinegar ratio of 2/3.

To make a dressing that is sweeter, we need a higher ratio of sugar to vinegar.

Here are some possible new measurements that would result in a sweeter dressing (greater than 0.67 ratio):

- If we try:
- Vinegar: 12 tbsp, Sugar: 9 tbsp → Ratio = 9/12 = 0.75 (sweeter)
- Vinegar: 18 tbsp, Sugar: 13 tbsp → Ratio = 13/18 ≈ 0.72 (sweeter)
- Vinegar: 24 tbsp, Sugar: 18 tbsp → Ratio = 18/24 = 0.75 (sweeter)
- Any other measurements that keep the amount of sugar greater relative to the vinegar (e.g. 12 tbsp vinegar with 10 tbsp sugar) will also result in a sweeter dressing.

Thus, to create a dressing that is sweeter than the original recipe, any ratio of sugar to vinegar that results in greater than 0.67 will work.