document.write( "Question 1203419: 12 ml of a 65% alcohol solution was mixed with 8 ml of an 80% alcohol solution. What is the concentration of the mixture?\r
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Algebra.Com's Answer #838964 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "In order to solve this problem and thousands other similar problems, a reader (a student)
\n" ); document.write( "should understand the method. In order for to get understanding, a reader (a student)
\n" ); document.write( "should hear (or read) right words describing right thoughts, at least once in his/her life,
\n" ); document.write( "instead of looking into tables with unknown purposes.\r
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document.write( "                  Solution\r\n" );
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document.write( "In this problem, there are three mixtures:\r\n" );
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document.write( "    - one   of 12 mL and 65% concentration;\r\n" );
document.write( "    - other of  8 mL and 80% concentration;\r\n" );
document.write( "    - third of 12+8 = 20 mL and unknown concentration.\r\n" );
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document.write( "Each concentration in this problem is the ratio of the alcohol volume to the volume of the relevant mixture.\r\n" );
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document.write( "So, to answer the problem's question, we should relate the alcohol volume in the final mixture\r\n" );
document.write( "to the volume of the final mixture.\r\n" );
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document.write( "The volume of the final mixture is the sum of the volumes of ingredients.\r\n" );
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document.write( "The alcohol volume in the final mixture is the sum of alcohol volumes in ingredients.\r\n" );
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document.write( "12 mL of the 65% alcohol solution contribute 0.65*12 milliliters of alcohol to the final mixture.\r\n" );
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document.write( "8 mL of the 80% alcohol solution contribute 0.8*8 milliliters of alcohol to the final mixture.\r\n" );
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document.write( "So, the final mixture has  0.65*12 + 0.8*8  milliliters of alcohol from ingredients.\r\n" );
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document.write( "Therefore, we write for the final concentration\r\n" );
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document.write( "     = .\r\n" );
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document.write( "Having the expression, it is easy to get the number. it is\r\n" );
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document.write( "     = 0.71, or 71%.\r\n" );
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document.write( "ANSWER.  The final concentration is 71%.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Now you are armed (your mind is charged) to solve hundreds and thousands similar problems.\r
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\n" ); document.write( "\n" ); document.write( "By knowing the general mantra, you may write your solutions in the future
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\n" ); document.write( "\n" ); document.write( "So, when you will get an expert level (after solving 3 - 5 similar problems),
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\n" ); document.write( "\n" ); document.write( " $\"C%5Bfinal%5D\"$ = $\"%280.65%2A12+%2B+0.8%2A8%29%2F%2812%2B8%29\"$ = 0.71.\r
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\n" ); document.write( "\n" ); document.write( "Memorize this logic, this mantra and the structure of this formula.\r
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