A chef plans to mix 100% vinegar with Italian dressing. The Italian dressing contains 4% vinegar. The chef wants to make 320 milliliters of a mixture that contains 13% vinegar. How much vinegar and how much Italian dressing should she use?

Answer: vinegar: 30 mL

Italian dressing: 290 mL

Step-by-step explanation:

100% vinegar + 4% Italian dressing

He wants 320 mL of mix with 13% vinegar → 320*0.13 = 41.6 mL

So, the mixture must have 41.6 mL of vinegar and 278.4 mL of other ingredients of the Italian Dressing (-vinegar). This way:

Let's call Italian dressing x and vinegar y:

4%x + 100%y = 41.6

96%x = 278.4

0.96x = 278.4

x = 278.4/0.96

x = 290

So, 290 mL of Italian dressing.

As he wants 320 of mixture, 320 - 290 = 30 mL of vinegar.

Italian dressing: 290 mL (11.6 mL vinegar)

100% Vinegar: 30 mL

Vinegar = 30 + 11.6 = 41.6 mL

320.13% = 41.6 mL (ok)