A chef is going to use a mixture of two brands of Italian dressing. The first brand contains 8% vinegar, and the second brand contains 13% vinegar. The chef wants to make 290 milliliters of a dressing that is 12% vinegar. How much of each brand should she use?

Let f and s denote the amounts of the first and second brands that the chef is going to use.

She wants to end up with 290 mL, so

f + s = 290

Each mL of the first brand contains 0.08 mL of vinegar, and each mL of the second contains 0.13 mL of vinegar. The final mixture should have a concentration of 12% vinegar, so that it contains 0.12 • 290 mL = 34.8 mL of vinegar, and

0.08f + 0.13s = 34.8

Solve for f and s :

f + s = 290   →   s = 290 - f

0.08f + 0.13 (290 - f ) = 34.8

0.08f + 37.7 - 0.13f = 34.8

0.05f = 2.9

f = 58

s = 290 - 58

s = 232