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 390 milliliters of a dressing that is 11 vinegar. How much of each brand should she use

Answer 1

Answer:

78 ml of 7% vinegar and 312 ml of 12% vinegar.

Step-by-step explanation:

Let x represent ml of 7% vinegar brand and y represent ml of 12% vinegar brand.    

We have been given that chef wants to make 390 milliliters of the dressing. We can represent this information in an equation as:

$x+y=390...(1)$

$y=390-x...(1)$

We are also told that 1st brand 7% vinegar, so amount of vinegar in x ml would be $0.07x$.

The second brand contains 12 vinegar, so amount of vinegar in y ml would be $0.12y$.

We are also told that the chef wants to make 390 milliliters of a dressing that is 11% vinegar. We can represent this information in an equation as:

$0.07x+0.12y=390(0.11)...(2)$

Upon substituting equation (1) in equation (2), we will get:

$0.07x+0.12(390-x)=390(0.11)$

$0.07x+46.8-0.12x=42.9$

$-0.05x+46.8=42.9$

$-0.05x+46.8-46.8=42.9-46.8$

$-0.05x=-3.9$

$\frac{-0.05x}{-0.05}=\frac{-3.9}{-0.05}$

$x=78$

Therefore, the chef should use 78 ml of the brand that contains 7% vinegar.

Upon substituting $x=78$ in equation (1), we will get:

$y=390-78$

$y=312$

Therefore, the chef should use 312 ml of the brand that contains 12% vinegar.