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
250
milliliters of a dressing that is
9%
vinegar. How much of each brand should she use?
To solve this problem, we can use a method called "mixture algebra." We can set up equations based on the given information and then solve for the unknown quantities.
Let's denote the amount of the first brand (6% vinegar) that the chef will use as "x" milliliters. Similarly, let's denote the amount of the second brand (11% vinegar) that the chef will use as "250 - x" milliliters (since the total volume of the dressing is 250 milliliters).
Now, let's write the equation based on the percentage of vinegar in the mixture:
(0.06 * x) + (0.11 * (250 - x)) = 0.09 * 250
Let's solve this equation step by step:
0.06x + (0.11 * 250) - (0.11x) = 0.09 * 250
0.06x - 0.11x + 27.5 = 22.5
-0.05x = -5
x = -5 / -0.05
x = 100
So, the chef should use 100 milliliters of the first brand (6% vinegar) and (250 - 100) = 150 milliliters of the second brand (11% vinegar) to make a 250 milliliter dressing with 9% vinegar.
add up the vinegar in each part:
.06x + .11(250-x) = .09(250)
...