Question

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 13% vinegar. The chef wants to make 320 milliliters of a dressing that is 11% vinegar. How much of each brand should she use?

Answer 1

let x = the brand of dressing with 5% vinegar

let y = the brand of dressing with 13% vinegar

Then

$\begin{gathered} x+y=320 \\ so \\ x=320-y \end{gathered}$

So,

$\begin{gathered} 0.05x+0.13y=0.11(320) \\ 0.05x+0.13y=35.2 \end{gathered}$

we replace x:

$\begin{gathered} 0.05(320-y)+0.13y=35.2 \\ 16-0.05y+0.13y=35.2 \\ 16+0.08y=35.2 \\ 16+0.08y-16=35.2-16 \\ 0.08y=19.2 \\ \frac{0.08y}{0.08}=\frac{19.2}{0.08} \\ y=240 \end{gathered}$

Therefore, for x:

$x=320-240=80$

Answer:

80 ml for 5% vinegar

240 ml for 13% vinegar