Question 1189875
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A chef is going to use a mixture of two brands of Italian dressing. 
The first brand contains 8% vinegar, and the second brand contains 13% vinegar. 
The chef wants to make 370 milliliters of a dressing that is 12% vinegar. 
How much of each brand should she use?
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<pre>
In this problem, concentrations are the ratios of the pure vinegar volume to the total volume.



Let x be the amount of the 8%  vinegar needed (in milliliters), and

let y be the amount of the 13%  vinegar needed.



The amount of the "pure" vinegar in the 8% mixture  is 0.08x mL.

The amount of the "pure" vinegar in the 13% mixture is 0.13y mL.

The resulting mixture contains  0.08x + 0.13y mL of the pure vinegar and has the volume of 370 mL.


Thus you have these two equations


    x + y = 370    milliliters           (1)    (the total volume)

    {{{(0.08x + 0.13y)/370}}} = 0.12.                 (2)    (the resulting mixture concentration)



From equation  (1), express  x = 370 - y.  Substitute it into equation (2) and multiply both sides of this equation by 370. 
You will get


    0.08*(370-y) + 0.13y = 0.12*370.


From the last equation express y and calculate


    y = {{{(0.12*370 - 0.08*370)/(0.13-0.08)}}} = 296 mL of the 13% vinegar are needed.


Then from equation (1),  x = 370 - 296 = 74 mL of the 8% vinegar are needed.


<U>Answer</U>. 296 mL of the 13% vinegar  and  74 mL of the 8% vinegar are  needed.


<U>Check</U>.  {{{(0.13*296 + 0.08*74)/370}}} = 0.12 = 12%.   ! Correct concentration !
</pre>

Solved.