SOLUTION: 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 milli

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)

     = 0.12.                 (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 =  = 296 mL of the 13% vinegar are needed.


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


Answer. 296 mL of the 13% vinegar  and  74 mL of the 8% vinegar are  needed.


Check.   = 0.12 = 12%.   ! Correct concentration !