document.write( "Question 1092146: How many liters of 80% alcohol solution and 40% alcohol solution must be mixed to obtain 12 liters of 50% alcohol solution? \n" ); document.write( "

Algebra.Com's Answer #706682 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "3 parts of the 40% and 1 part of the 80%, i.e. 9 liters of the 40% and 3 liters of the 80%, IF TO SOLVE THE PROBLEM MENTALLY\r
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\n" ); document.write( "\n" ); document.write( "Let's check: $\"%280.4%2A9+%2B+0.8%2A3%29%2F12\"$ = $\"%283.6+%2B+2.4%29%2F12\"$ = $\"6%2F12\"$ = 0.5 = 50%.\r
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\n" ); document.write( "\n" ); document.write( "Yes, it works.\r
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\n" ); document.write( "\n" ); document.write( "Now I'll show you how to solve it using equation.\r
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document.write( "Let x be the amount (the volume in liters) of the 40% solution.\r\n" );
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document.write( "Then the amount of the 80% solution is  (12-x) liters.\r\n" );
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document.write( "The \"alcohol contents/concentration equation\" is\r\n" );
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document.write( " = 0.5.\r\n" );
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document.write( "Multiply by 12 both parts:\r\n" );
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document.write( "0.4x + 0.8*(12-x) = 6  ====>\r\n" );
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document.write( "0.4x + 9.6 - 0.8x = 6  ====>\r\n" );
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document.write( "9.6 - 6 = 0.8x - 0.4x  ====>  0.4x = 3.6 ===>  x =  = 9.\r\n" );
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document.write( "So, we get the same answer: 9 liters of the 40% solution and (12-9) = 3 liters of the 80% solution.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "----------------
\n" ); document.write( "There is entire bunch of introductory lessons covering various types of mixture problems\r
\n" ); document.write( "\n" ); document.write( "    - Mixture problems\r
\n" ); document.write( "\n" ); document.write( "    - More Mixture problems\r
\n" ); document.write( "\n" ); document.write( "    - Solving typical word problems on mixtures for solutions \r
\n" ); document.write( "\n" ); document.write( "    - Word problems on mixtures for antifreeze solutions \r
\n" ); document.write( "\n" ); document.write( "    - Word problems on mixtures for alloys \r
\n" ); document.write( "\n" ); document.write( "    - Typical word problems on mixtures from the archive\r
\n" ); document.write( "\n" ); document.write( "in this site.\r
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\n" ); document.write( "\n" ); document.write( "Read them and become an expert in solution mixture word problems.\r
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\n" ); document.write( "\n" ); document.write( "Also, you have this free of charge online textbook in ALGEBRA-I in this site\r
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lessons are the part of this textbook in the section \"Word problems\" under the topic \"Mixture problems\".\r
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\n" ); document.write( "\n" ); document.write( "Save the link to this online textbook together with its description\r
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\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-I\r
\n" ); document.write( "\n" ); document.write( "https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson\r
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\n" ); document.write( "\n" ); document.write( "to your archive and use it when it is needed.\r
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