document.write( "Question 1203015: How many liters of water must be added to 20 liters of a 20%salt solution to make it a 12.5 % salt solution\r
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Algebra.Com's Answer #838260 by ikleyn(52776)\"\" \"About 
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\n" ); document.write( "\n" ); document.write( "        It is one of standard mixture problems. Solving mixture problems and relevant teaching
\n" ); document.write( "        (as for many other Math problems) requires not only correct manipulating with numbers.\r
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\n" ); document.write( "\n" ); document.write( "        Full/comprehensive understanding requires using correct terms, notions, conceptions, and the measurement units.
\n" ); document.write( "        It is why I came to explain you everything related to this problem using right terminology.\r
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document.write( "The word \"salt\" in this problem describes either a solid substance or dry crumbly substance \r\n" );
document.write( "like sand.\r\n" );
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document.write( "Its amount is NEVER measured in liters, which is the unit to measure fluid volumes.\r\n" );
document.write( "In Science, technique, industry its amount is ALWAYS measured in MASS units, like grams, kilograms etc.\r\n" );
document.write( "In this problem, where the volume of water is measured in liters, an appropriate unit\r\n" );
document.write( "to measure an amount of salt is kilogram.\r\n" );
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document.write( "So, in this problem, all concentrations are kg/liter (kilograms per liters), \r\n" );
document.write( "which is mass to volume unit.\r\n" );
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document.write( "The original 20% salt solution contains  20*0.2 = 4 kilograms of salt dissolved.\r\n" );
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document.write( "Since we add pure water with no salt, this amount of dissolved salt of 4 kg remains unchanged:\r\n" );
document.write( "in the final solution we have the same mass of salt dissolved.\r\n" );
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document.write( "The final solution should be 12.5% concentration.  It means that the volume V \r\n" );
document.write( "of the final mixture must be \"4%2FV\" = 0.125,  or  V = \"4%2F0.125\" = 32 liters.\r\n" );
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document.write( "Thus, the volume of the pure water to add is this difference 32 - 20 = 12 liters.\r\n" );
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document.write( "ANSWER.  12 liters of water should be added.\r\n" );
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\n" ); document.write( "\n" ); document.write( "        The solution presented above is based on common sense (= on the mass conservation law).\r
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\n" ); document.write( "\n" ); document.write( "        For completeness purposes, I present below another solution based on simple algebra equation.\r
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document.write( "Let x be the volume of the pure water to add, in liters.\r\n" );
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document.write( "Write equation for the salt amount, which is the same in the original and final mixture\r\n" );
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document.write( "    0.2*20 = 0.125*(20+x).\r\n" );
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document.write( "Left side is the dissolved salt amount in the original 20 liters of the 20% mixture.\r\n" );
document.write( "Right side is the dissolved salt amount in the final (20+x) liters of the 12.5% mixture.\r\n" );
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document.write( "Solving this equation is easy\r\n" );
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document.write( "    4 = 2.5 + 0.125x\r\n" );
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document.write( "    4 - 2.5 = 0.125x\r\n" );
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document.write( "       1.5   = 0.125x\r\n" );
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document.write( "       x     = 1.5/0.125 = 12.\r\n" );
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document.write( "You get the same answer as in the solution above: 12 liters of water should be added.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved in two ways, with accurate explanations.\r
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\n" ); document.write( "\n" ); document.write( "To see many other similar solved problems, look into the lessons\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
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\n" ); document.write( "\n" ); document.write( "    - Special type mixture problems on DILUTION adding water\r
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\n" ); document.write( "\n" ); document.write( "Learn EVERYTHING related to mixture problems from these lessons.\r
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