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

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

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`

`(-0.05x)/(-0.05)=(-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.