Question

A chef is going to use a mixture of two brands of Italian dressing. The first brand contains 7% vinegar, and the second brand contains 12% vinegar. The chef wants to make 320 milliliters of a dressing that is 9% vinegar. How much of each brand should she use?

Answer 1

Answer:F + S = 124

Explanation:

Also, you want the total mixture to contain 8% vinegar so: .06F + .11S = .08(310)

Now, we can solve the system of equations using substitution.

F + S = 310

.06F + .11S = .08(310)

F = 310 - S [solve 1st equation for F]

.06(310 - S) + .11S = .08(310) [substitute into 2nd equation]

18.6 -.06S +.11S = 24.8

.05S = 6.2

S = 124

Answer 2

To create a 9% vinegar mixture, the chef should use 192 milliliters of the first brand (7% vinegar) and 128 milliliters of the second brand (12% vinegar).

The student is asking how to mix two brands of Italian dressing to create 320 milliliters of dressing with a 9% vinegar concentration. One brand has 7% vinegar, and the other has 12% vinegar.

To solve this, we let x be the amount of the first brand (7% vinegar) and 320 - x be the amount of the second brand (12% vinegar). The total amount of vinegar from both brands should equal 9% of the total solution (320 milliliters).

We can set up the equation: 0.07x + 0.12(320 - x) = 0.09 \( 320 \) and solve for x.

Multiplying out the terms gives us:

0.07x + 38.4 - 0.12x = 28.8

Combining like terms gives us:

-0.05x + 38.4 = 28.8

Solving for x, we find:

x = (38.4 - 28.8) / 0.05

x = 192 milliliters of the first brand and 320 - 192 = 128 milliliters of the second brand.