A chef is going to use a mixture of two brands of Italian dressing. The first brand contains 6% vinegar, and the second brand contains 11% vinegar. The chef wants to make 210 milliliters of a dressing that is 8% vinegar. How much of each brand should she use?
Let's denote the amount of the first brand of Italian dressing as x milliliters and the amount of the second brand as 210 - x milliliters.
To find the amount of vinegar in the final mixture, we need to multiply the vinegar percentage of the first brand by the number of milliliters used, and do the same for the second brand, and then add the two amounts together.
For the first brand, the amount of vinegar is 6/100 * x = 0.06x milliliters.
For the second brand, the amount of vinegar is 11/100 * (210 - x) = 0.11(210 - x) milliliters.
For the final mixture, the amount of vinegar is 8/100 * 210 = 0.08 * 210 = 16.8 milliliters.
Since we want to have 8% vinegar in the final mixture, we can set up the equation:
0.06x + 0.11(210 - x) = 16.8
Expanding the equation, we get:
0.06x + 23.1 - 0.11x = 16.8
Combining like terms, we get:
-0.05x + 23.1 = 16.8
Subtracting 23.1 from both sides, we get:
-0.05x = -6.3
Dividing both sides by -0.05, we get:
x = -6.3 / -0.05
x = 126
Therefore, the chef should use 126 milliliters of the first brand and (210 - 126) = <<210-126=84>>84 milliliters of the second brand.