SOLUTION: A chef plans to mix 100% vinegar with Italian dressing. The Italian dressing contains 13% vinegar. The chef wants to make 150 milliliters of a mixture that contains 42% vinegar. Ho

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Question 1204015: A chef plans to mix 100% vinegar with Italian dressing. The Italian dressing contains 13% vinegar. The chef wants to make 150 milliliters of a mixture that contains 42% vinegar. How much vinegar and how much Italian dressing should she use?
Found 2 solutions by ikleyn, josgarithmetic:
Answer by ikleyn(52812) About Me  (Show Source):
You can put this solution on YOUR website!
.
A chef plans to mix 100% vinegar with Italian dressing. The Italian dressing contains 13% vinegar.
The chef wants to make 150 milliliters of a mixture that contains 42% vinegar.
How much vinegar and how much Italian dressing should she use?
~~~~~~~~~~~~~~~~~~~ 

Let x be the volume (in milliliters) of the 100% vinegar to mix with Italian dressing.

Then the volume of the Italian dressing should be (150-x) milliliters.


The total volume will be x + (150-x) milliliters;

the volume of the vinegar will be  [0.13*(150-x) + x].


We want the final mixture be 42% vinegar.  It means

    0.13*(150-x) + x = 0.42*150.


To find x, simplify step  by step

    0.13*150 - 0.13x + x = 0.42*150

    x - 0.13x = 0.42*150 - 0.13*150

       x = %280.42%2A150+-+0.13%2A150%29%2F0.87 = 50.


ANSWER.  50 milligrams of the 100% vinegar should be added.

Solved.

-----------------

It is a standard and typical mixture problem.

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Start from these introductory lessons

    - Mixture problems
    - More Mixture problems
    - Solving typical word problems on mixtures for solutions
    - Typical word problems on mixtures from the archive

You will find there ALL TYPICAL mixture problems with different methods of solutions,
explained at different levels of detalization,  from very detailed to very short.

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Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
M mililiters of result mixture using
v miiliters of straight vinegar
M-v mililiters of the Italian Dressing, L% vinegar
-
T % vinegar in resulting mixture



highlight_green%28100v%2BL%28M-v%29=TM%29

100v-Lv%2BML=MT
%28100-L%29v=MT-ML
highlight_green%28v=M%28%28T-L%29%2F%28100-L%29%29%29

Substituting the given values, highlight%28v=150%28%2842-13%29%2F%28100-13%29%29%29
v=150%2829%2F87%29
v=150%281%2F3%29
highlight%28v=50%29----------ml. of the 100% vinegar