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 220 milliliters of a dressing that is 13% vinegar. How much of each brand should she use?

Answer 1

Let:

x = Amount of first brand

y = Amount of second brand

so:

`0.09x+0.14y=0.13(220)`

where:

`y=220-x`

So:

`\begin{gathered} 0.09x+0.14(220-x)=28.6 \\ 0.09x+30.8-0.14x=28.6 \\ -0.05x=28.6-30.8 \\ -0.05x=-2.2 \\ x=(-2.2)/(-0.05) \\ x=44 \end{gathered}`

so:

`\begin{gathered} y=220-44 \\ y=176 \end{gathered}`

Answer:

44 mm of the first brand

176 mm of the second brand