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 340milliliters of a dressing that is 12% vinegar. How much of each brand should she use?

Answer 1

Let us denote by x the milliliters of 9% vinegar to be used in the mixture. Then, the following amount

`340\text{ - }x\text{ }`

is the number of milliliters of 14% vinegar to be used in the mixture.

Taking this into account, we obtain the following equation:

`0.09\text{ x }+0.14(340-x)=0.12(340)\text{ }`

this is equivalent to:

`0.09\text{ x -0.14 x + 47.6 = 40.8}`

this is equivalent to:

`-0.05\text{ x = -6.8}`

or

`0.05x\text{ = 6.8}`

solving for x, we get:

`x\text{ = }(6.8)/(0.05)=\text{ 136}`

so that, the correct answer is:

ml of 9% vinegar to be used in mixture= 136 ml

ml of 14% vinegar to be used in mixture = 340 ml - 136 ml = 204 ml