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 360 milli

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Question 1195876: 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 360 milliliters of a dressing that is 13% vinegar. how much of each brand should she use?
Found 3 solutions by ikleyn, greenestamps, josgarithmetic:
Answer by ikleyn(52803) About Me  (Show Source):
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.
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 360 milliliters of a dressing that is 13% vinegar.
how much of each brand should she use?
~~~~~~~~~~~~~~~~ 

Take x mL of the 14% vinegar and (360-x) mL of the 9% vinegar.


Write the volume balance equation for the pure vinegar

    0.14x + 0.09*(360-x) = 0.13*360   mL.


Simplify and find x

    0.14x + 0.09*360 - 0.09x = 0.13*360

    0.14x - 0.09x = 0.13*360 - 0.09*360

    (0.14 - 0.09)x =      14.4

         0.05x     =      14.4

             x     =      14.4/0.05 = 288 mL.


ANSWER.  She should take 288 mL of the 14% vinegar and (360-288) = 72 mL of the 9% vinegar.

Solved.



Answer by greenestamps(13200) About Me  (Show Source):
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Here is a simple non-algebraic way to solve a two-part "mixture" problem like this that gets the answer to this particular example very fast, because the numbers are "nice".

Observe (perhaps using a number line, if it helps) that 13% is 4/5 of the way from 9% to 14%.
That means 4/5 of the mixture is the one with 14% vinegar.

ANSWER: 4/5 of 360ml, or 288ml, of the 14% vinegar dressing; the other 72ml of the 9% vinegar dressing.

Answer by josgarithmetic(39620) About Me  (Show Source):
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FirstBrand, L % vinegar
SecondBrand, H % vinegar
M ml. of T % vinegar wanted
If using v ml. of the SecondBrand, then M-v ml. of FirstBrand.

highlight_green%28L%28M-v%29%2BHv=TM%29
LM-Lv%2BHv=TM
Hv-Lv=TM-LM
v%28H-L%29=M%28T-L%29
highlight%28v=M%28%28T-L%29%2F%28H-L%29%29%29

Given information
L=9
H=14
T=13
M=360
-
Unknown information
v, how much of the H % vinegar dressing