SOLUTION: A chef is going to use a mixture of two brands of Italian dressing. The first brand contains 6% vinegar, and the second brand contains 12% vinegar. The chef wants to make 240 milli

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Question 1142572: A chef is going to use a mixture of two brands of Italian dressing. The first brand contains 6% vinegar, and the second brand contains 12% vinegar. The chef wants to make 240 milliliters of a dressing that is 7% vinegar. How much of each brand should she use?
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
One sixth of the way from one to the other

0.06%28240-x%29%2B0.12x=0.07%2A240, x being volume of the 12% vinegar material.

6%28240-x%29%2B12x=7%2A240
6%2A240-6x%2B12x=7%2A240
6x=7%2A240-6%2A240
6x=240%287-6%29
highlight_green%28x=240%28%287-6%29%2F6%29%29

x=240%281%2F6%29-----------------one sixth of 240, the amount for the 12% vinegar

Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


Here is an alternative to the standard algebraic method for solving mixture problems like this. If you understand it (and if an algebraic solution is not required), it will get you to the answers to problems like this much faster and with much less effort.

(1) the difference between the 6% and 12% of the two ingredients is 6%; the difference between the 6% of the first ingredient and the 7% of the mixture is 1%.

So the 7% target concentration is 1/6 of the way from 6% to 12%.

That means 1/6 of the mixture needs to be the ingredient with 12% vinegar.

ANSWER: 1/6 of 240ml = 40ml of 12%; the other 5/6 of 240ml, or 200 ml, of 6%.