Question

A chef is going to use a mixture of two brands of Italian dressing. The first brand contains 9% vinegar, and the second brand contains 14% vinegar. The chef wants to make 230 milliliters of a dressing that is 13% vinegar. How much of each brand should she use?

Answer 1

So, the first brand has 9% vinegar, and say we use "x" amount of it, then, the amount of vinegar in "x" is 9% of x, or (9/100) * x, 0.09x.

the second brand has 14% of vinegar, and if we use say "y" amount of it, then the amount of vinegar in "y" is really just 14% of "y" or, (14/100) * y, 0.14y.

$\bf \begin{array}{lccclll} &\stackrel{mL}{amount}&\stackrel{\%}{concentration}&\stackrel{amount}{concentration}\\ &------&------&------\\ \textit{first brand}&x&0.09&0.09x\\ \textit{second brand}&y&0.14&0.14y\\ ------&------&------&------\\ mixture&230&0.13&29.9 \end{array}$

so, whatever "x" and "y" are, we know that x + y = 230.

and we also know that their concentration amounts will also add up,  0.09x + 0.14y = 29.9.

$\bf \begin{cases} x+y=230\implies \boxed{y}=230-x\\ 0.09x+0.14y=29.9\\ ----------\\ 0.09x+0.14\left(\boxed{230-x} \right)=29.9 \end{cases} \\\\\\ 0.09x+32.2-0.14x=29.9\implies -0.05x=-2.3\implies x=\cfrac{-2.3}{-0.05} \\\\\\ x=46$

how many milliliters will it be for the second brand?  well, y = 230 - x.