Question

a chef is going to use a mixture of two brands of Italian dressing. the first brand contains 6% vinegar, and the second brand contains 9% vinegar. the chef wants to make 210 mL of a dressing that is 8% vinegar. how much of each branch should she use?First brand: __ milliliterssecond brand: __ milliliters

Answer 1

Answer:

• First brand: 70 milliliters

,

• Second brand: 140 milliliters​

Explanation:

• Let the volume of the first brand used = x mL

Since the volume of dressing the chef wants to make is 210 mL:

• The volume of the second brand = (210-x)mL

This gives rise to the equation:

$(6\%\text{ of x)+}(9\%\text{ of (210-x))}=8\%\text{ of 210}$

Next, solve for x:

$\begin{gathered} 0.06x+0.09(210-x)=0.08\times210 \\ 0.06x+18.9-0.09x=16.8 \\ 0.06x-0.09x=16.8-18.9 \\ -0.03x=-2.1 \\ x=\frac{-2.1}{-0.03} \\ x=70mL \end{gathered}$

Thus, for the first brand, he should use 70 mL.

For the second brand, he should use (210-70) = 140 mL.