contestada

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?

Respuesta :

Solution:

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

[tex]340\text{ - }x\text{ }[/tex]

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

Taking this into account, we obtain the following equation:

[tex]0.09\text{ x }+0.14(340-x)=0.12(340)\text{ }[/tex]

this is equivalent to:

[tex]0.09\text{ x -0.14 x + 47.6 = 40.8}[/tex]

this is equivalent to:

[tex]-0.05\text{ x = -6.8}[/tex]

or

[tex]0.05x\text{ = 6.8}[/tex]

solving for x, we get:

[tex]x\text{ = }\frac{6.8}{0.05}=\text{ 136}[/tex]

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

Otras preguntas