Respuesta :
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:
[tex]x+y=390...(1)[/tex]
[tex]y=390-x...(1)[/tex]
We are also told that 1st brand 7% vinegar, so amount of vinegar in x ml would be [tex]0.07x[/tex].
The second brand contains 12 vinegar, so amount of vinegar in y ml would be [tex]0.12y[/tex].
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:
[tex]0.07x+0.12y=390(0.11)...(2)[/tex]
Upon substituting equation (1) in equation (2), we will get:
[tex]0.07x+0.12(390-x)=390(0.11)[/tex]
[tex]0.07x+46.8-0.12x=42.9[/tex]
[tex]-0.05x+46.8=42.9[/tex]
[tex]-0.05x+46.8-46.8=42.9-46.8[/tex]
[tex]-0.05x=-3.9[/tex]
[tex]\frac{-0.05x}{-0.05}=\frac{-3.9}{-0.05}[/tex]
[tex]x=78[/tex]
Therefore, the chef should use 78 ml of the brand that contains 7% vinegar.
Upon substituting [tex]x=78[/tex] in equation (1), we will get:
[tex]y=390-78[/tex]
[tex]y=312[/tex]
Therefore, the chef should use 312 ml of the brand that contains 12% vinegar.
