a chef is going to use a mixture of two brands of Italian dressing. the first brand contains 5% vinegar, and the second brand contains 8% vinegar. the chef wants to make 300 milliliters of a dressing that is 6% vinegar. how much of each branch should she use?First brand: milliliters Second brand: milliliters

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TremaineK526060 TremaineK526060 · Answer 1 · 2022-10-31T05:55:16+01:00

Let A be the first brand and B the second brand, then, we can write

[tex]\begin{gathered} 0.05A+0.08B=0.06\times300\ldots(a) \\ \text{and} \\ A+B=300\ldots(b) \end{gathered}[/tex]

so we have 2 equations in 2 unknows.

Solving by substitution method.

By moving B to the right hand side in the second equation, we have

[tex]A=300-B\ldots(c)[/tex]

By substituting this result into equation (a), we have

[tex]0.05(300-B)+0.008B=18[/tex]

where 18 = 0.06x300. By combining similar terms, we get

[tex]\begin{gathered} 15-0.05B+0.08B=18 \\ 15+0.03B=18 \end{gathered}[/tex]

By moving 15 to the right hand side, we obtain

[tex]\begin{gathered} 0.03B=18-15 \\ 0.03B=3 \end{gathered}[/tex]

then, B is equal to

[tex]\begin{gathered} B=\frac{3}{0.03} \\ B=100 \end{gathered}[/tex]

Now, by substituting this result into equation (c), we have

[tex]\begin{gathered} A=300-100 \\ A=200 \end{gathered}[/tex]

This implies tha the answer is:

First brand: 200 mililiters

Second brand: 100 mililiters