SOLUTION: How many quarts of pure alcohol should be added to 10 quarts of 10% alcohol solution to obtain a mixture of 25% alcohol?

Question 1194698: How many quarts of pure alcohol should be added to 10 quarts of 10% alcohol solution to obtain a mixture of 25% alcohol?

Found 3 solutions by ikleyn, josgarithmetic, greenestamps:
Answer by ikleyn(52787)   (Show Source): You can put this solution on YOUR website!
.
How many quarts of pure alcohol should be added to 10 quarts of 10% alcohol solution
to obtain a mixture of 25% alcohol?
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Initially, we have 10 quarts of 10% acohol solution. It contains, obviously, 1 quarts of pure alcohol and 10-1 = 9 quarts of water. When we add pure alcohol, the water contents of 9 quarts remains uncheanged. So, in the new mixture, 9 quarts of water should comprise 75% of liquid. Hence, the total volume of the mixture should be = = 3*4 = 12 quarts. It means that 12-10 = 2 quarts of the pure alcohol should be added. ANSWER

Solved.

It can be solved in other way/(ways), too, but I presented here the MENTAL solution.

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On solving mixture problems, see the lessons

    - Mixture problems
    - More Mixture problems
    - Solving typical word problems on mixtures for solutions

    - Special type mixture problems on DILUTION adding water
    - Increasing concentration of an acid solution by adding pure acid

in this site.

Read them and become an expert in solution the mixture word problems.

Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Mixture problems".

Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.

Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
Q quarts to add

Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

Here is another way you can solve any 2-part "mixture" problem like this mentally, if your mental arithmetic skills are good.

You are starting with a 10% alcohol solution and adding 100% alcohol, stopping when you get to 25%.

Picture that as "walking" on the number line from 10 towards 100, stopping when you get to 25. The total distance of that walk was 100-10=90; you stopped when the distance you had traveled was 25-10=15.

Here is the key to this method:
******************************************************************** * The fraction of the total distance you traveled was 15/90 = 1/6; * * that means 1/6 of the final mixture is what you ADDED. * ********************************************************************

Since 1/6 of the final mixture is the 100% alcohol you added, the 10 quarts of 10% alcohol you started with is 5/6 of the mixture; that means you added 2 quarts of 100% alcohol.

The words of explanation make this sound like a long and difficult process; but without the words the calculations are quick and easy:

100-10=90; 25-10=15; 15/90 = 1/6
1-1/6 = 5/6
5/6 = 10 quarts --> 1/6 = 2 quarts

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