A chef wants to make 1 gallon (128 ounces) of a 15% vinegar-to-oil salad dressing. He only has pure vinegar and a mild 4% vinegar-to-oil salad dressing on hand. How many ounces of each should he mix to make the desired dressing

Pure vinegar: 12.2 ounces, 4% mix salad: 115.8 ounces

Explanation:

The chef wants to male a 15% vinegar-to-oil salad.

If we call:

the amount of vinegar in the salad

the amount of oil in the salad

This means that

In order to get this salad, the chef has to mix:

- Pure vinegar, which has 100% concentration of vinegar

- A 4% vinegar-to-oil salad: this means that the amount of vinegar in this salad is (4% of the amount of oil)

This means that the total amount of vinegar in the final salad will be:

(1a)

Where v is the amount of pure vinegar added and is the amount of oil in the 4% salad

While the amount of oil needed is

So we have, since the final salad has 15% concentration of vinegar to oil:

(1)

Moreover, we know that the final volume must be 128 ounces, so

(2)

From eq.(2) and (1a) we get

Substituting into (1) and solving for ,

Therefore the amount of vinegar must be

So, the amount of each that should be added is:

- Pure vinegar: 12.2 ounces

- 4% vinegar-to-oil mix: ounces

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