.
In order to solve this problem and thousands other similar problems, a reader (a student)
should understand the method. In order for to get understanding, a reader (a student)
should hear (or read) right words describing right thoughts, at least once in his/her life,
instead of looking into tables with unknown purposes.
Solution
In this problem, there are three mixtures:
- one of 12 mL and 65% concentration;
- other of 8 mL and 80% concentration;
- third of 12+8 = 20 mL and unknown concentration.
Each concentration in this problem is the ratio of the alcohol volume to the volume of the relevant mixture.
So, to answer the problem's question, we should relate the alcohol volume in the final mixture
to the volume of the final mixture.
The volume of the final mixture is the sum of the volumes of ingredients.
The alcohol volume in the final mixture is the sum of alcohol volumes in ingredients.
12 mL of the 65% alcohol solution contribute 0.65*12 milliliters of alcohol to the final mixture.
8 mL of the 80% alcohol solution contribute 0.8*8 milliliters of alcohol to the final mixture.
So, the final mixture has 0.65*12 + 0.8*8 milliliters of alcohol from ingredients.
Therefore, we write for the final concentration
= .
Having the expression, it is easy to get the number. it is
= 0.71, or 71%.
ANSWER. The final concentration is 71%.
Solved.
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Now you are armed (your mind is charged) to solve hundreds and thousands similar problems.
By knowing the general mantra, you may write your solutions in the future
in much shorter form, keeping explanations in your mind and writing the formulas only.
So, when you will get an expert level (after solving 3 - 5 similar problems),
your solution will be in one line
= = 0.71.
Memorize this logic, this mantra and the structure of this formula.