Question 1204015
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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?
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<pre>
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 = {{{(0.42*150 - 0.13*150)/0.87}}} = 50.


<U>ANSWER</U>.  50 milligrams of the 100% vinegar should be added.
</pre>

Solved.


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It is a standard and typical mixture problem.


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