A chef is using a mixture of two brands of Italian dressing. The first brand contains 7% vinegar, and the second brand contains 11% vinegar. The chef wants to make 280 milliliters of a dressing that is 10% vinegar. How much of each brand should she use?

first brand?
second brand?

To find out how much of each brand of Italian dressing the chef should use, we can set up a system of equations based on the given information.

Let's say x represents the amount (in milliliters) of the first brand, and y represents the amount of the second brand.

From the problem statement, we know that the chef wants to make 280 milliliters of a dressing that is 10% vinegar. This means that the amount of vinegar in the final mixture should be 10% of 280, which is 28 milliliters.

Now, we can set up the equations based on the vinegar content in each brand of the dressing.

For the first brand, since it contains 7% vinegar, the amount of vinegar in the first brand is 7% of x, or 0.07x.

Similarly, for the second brand, the amount of vinegar in the second brand is 11% of y, or 0.11y.

We can now set up the equation based on the total vinegar content:

0.07x + 0.11y = 28 (equation 1)

Next, we need to set up an equation that represents the total volume of the dressing:

x + y = 280 (equation 2)

Now we have a system of two equations with two unknowns. We can solve this system to find the values of x and y.

One way to solve this system is by using substitution or elimination.

Let's use substitution:

From equation 2, we can express x in terms of y:

x = 280 - y

Now, substitute this expression for x in equation 1:

0.07(280 - y) + 0.11y = 28

Multiply through the equation:

19.6 - 0.07y + 0.11y = 28

Combine like terms:

0.04y = 8.4

Divide both sides by 0.04:

y = 210

Now, substitute this value of y back into the expression for x:

x = 280 - 210

x = 70

Therefore, the chef should use 70 milliliters of the first brand and 210 milliliters of the second brand to make a dressing that is 10% vinegar.