Question 1194698
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Here is another way you can solve any 2-part "mixture" problem like this mentally, if your mental arithmetic skills are good.<br>
You are starting with a 10% alcohol solution and adding 100% alcohol, stopping when you get to 25%.<br>
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.<br>
Here is the key to this method:<br><pre>
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* 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.         *
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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.<br>
The words of explanation make this sound like a long and difficult process; but without the words the calculations are quick and easy:<br>
100-10=90; 25-10=15; 15/90 = 1/6
1-1/6 = 5/6
5/6 = 10 quarts  -->  1/6 = 2 quarts<br>