SOLUTION: 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 270 millil

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: 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 270 millil      Log On


   

Question 1182079: 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 270 milliliters of a dressing that is 11%vinegar. how much of each brand should she use?
Found 3 solutions by josgarithmetic, MathTherapy, greenestamps:
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
v ml. of the 14%
270-v ml. of the 9%

14v%2B9%28270-v%29=11%2A270
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14v%2B9%2A270-9v=11%2A270
%2814-9%29v%2B9%2A270=11%2A270
%2814-9%29v=11%2A270-9%2A270
v=%2811%2A270-9%2A270%29%2F%2814-9%29
highlight%28v=270%28%2811-9%29%2F%2814-9%29%29%29-------------simple to compute
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..., mixture of two brands of Italian dressing. the first brand contains L % vinegar, and the second brand contains H % vinegar. the chef wants to make M milliliters of a dressing that is T % vinegar. how much of each brand,...?
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v, amount of H %
M-v, amount of L %

highlight_green%28Hv%2BL%28M-v%29=TM%29, accounting for amount of pure material

Hv%2BLM-Lv=TM
Hv-Lv=TM-LM
%28H-L%29v=M%28T-L%29
highlight%28v=M%28%28T-L%29%2F%28H-L%29%29%29----------substitute your given or known values and evaluate; and then use to evaluate M-v.

Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!

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 270 milliliters of a dressing that is 11%vinegar. how much of each brand should she use?
Let amount of 9% to be mixed, be N

Then amount of the 14% concentration to be mixed = 270 - N

We then get: .09N + .14(270 - N) = .11(270)

              .09N + 37.8 - .14N = 29.7

                     .09N - .14N = 29.7 - 37.8

                          - .05N = - 8.1

Amount of 9% to be mixed, or 

You should now be able to determine the amount of the 14% to mix!!

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


If you love magic formulas that give you the answer to a problem without teaching you anything about HOW to get the answer, memorize and use the formula shown in the second part of the response from @josgartihmetic.

If you want to learn the standard algebraic approach to solving this kind of problem -- and to be able to understand HOW that method gets you the answer -- use what that tutor shows in the first part of their response, or the similar method shown in the response from tutor @MathTherapy.

If you want a faster method for finding the answer without formal algebra, consider the following.

The ratio in which the two ingredients need to be mixed is exactly determined by where the percentage of the mixture lies between the percentages of the two ingredients.

For example, to solve this problem by this method, you only need to do this:
(1) observe that 11% is 2/5 of the way from 9% to 14% (picturing the three percentages on a number line might help see this)
(2) that means 2/5 of the mixture is the 14% ingredient

ANSWER: 2/5 of 270ml, or 108ml, of 14% vinegar; the other 3/5 of the mixture, 162ml, of the 9% vinegar.