document.write( "Question 1051159: a chemist needs 25 liters of a 10% alcohol solution but has only a 25% alcohol solution. how many liters each of the 25% solution and water should he mix to make the desired 25 liters of 10% solution? \n" ); document.write( "

Algebra.Com's Answer #666738 by ikleyn(52787) $\"\"$ $\"About$

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\n" ); document.write( "a chemist needs 25 liters of a 10% alcohol solution but has only a 25% alcohol solution.
\n" ); document.write( "how many liters each of the 25% solution and water should he mix to make the desired 25 liters of 10% solution?
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\n" ); document.write( "\n" ); document.write( "Solution 1. One equation in one unknown.\r
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document.write( "Let W be the volume of water in liters to mix with the 25% alcohol.\r\n" );
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document.write( "Then the volume of the 25% alcohol solution is (25-W) liters.\r\n" );
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document.write( "The \"alcohol content\" equation is \r\n" );
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document.write( "0.25*(25-W) = 0.1*25,     (1)   \r\n" );
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document.write( "or\r\n" );
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document.write( "6.25 - 0.25W = 2.5  --->  -0.25W = 2.5 - 6.25  --->  -0.25W = 15.\r\n" );
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document.write( "15 liters of water is needed.\r\n" );
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document.write( "Answer.  Mix 25-15 = 10 liters of the 25% alcohol and 15 liters of water, and you will get 25 liters of the 10% alcohol.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solution 2. Two equations in two unknown.\r
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document.write( "Let W be the volume of water in liters to mix with the 25% alcohol.\r\n" );
document.write( "Let A be the volume of the 50% alcohol to mix.\r\n" );
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document.write( "Then the volume equation is \r\n" );
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document.write( "A + W = 25             (1)\r\n" );
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document.write( "The \"alcohol content\" equation is\r\n" );
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document.write( "0.25A = 0.1*25.        (2)\r\n" );
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document.write( "Express A = 25-W from (1) and substitute it into (2). You will get\r\n" );
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document.write( "0.25(25-W) = 0.*25.    (3)\r\n" );
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document.write( "This equation coincides with the equation (1) of the Solution 1 above and, hence, has the same solution.\r\n" );
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document.write( "So, in this way you get the same answer.\r\n" );
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\n" ); document.write( "\n" ); document.write( "There is entire bunch of the 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 the 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( "The textbook contains many other solved word problems, as well as many other interesting and useful things.\r
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