document.write( "Question 1187114: When 1 kg of salt is added to a solution and water, the solution becomes 33 1/3 % salt by mass. When 1 kg of water is added to the new solution, the resulting solution is 30% by mass. The percentage of salt in the original solution is? Can someone please solve this question?
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Algebra.Com's Answer #818068 by ikleyn(52781)\"\" \"About 
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\n" ); document.write( "When 1 kg of salt is added to a solution and water, the solution becomes 33 1/3 % salt by mass.
\n" ); document.write( "When 1 kg of water is added to the new solution, the resulting solution is 30% by mass.
\n" ); document.write( "The percentage of salt in the original solution is? Can someone please solve this question?
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document.write( "Let x be the mass of salt (in kilograms), and let w be the mass of water (in kilograms) in the original solution.\r\n" );
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document.write( "Then from the problem's description, we have these equations for mass concentrations\r\n" );
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document.write( "    \"%28x%2B1%29%2F%28x%2B1%2Bw%29\"    = \"1%2F3\",      (1)\r\n" );
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document.write( "    \"%28x%2B1%29%2F%28x%2B1%2Bw%2B1%29\" = \"3%2F10\".     (2)\r\n" );
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document.write( "From these equations, we have further\r\n" );
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document.write( "    3(x+1)   = x + w  + 1                   \r\n" );
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document.write( "    10*(x+1) = 3(x + w + 2)                   \r\n" );
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document.write( "Continue transformations\r\n" );
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document.write( "     3x +  3 = x + w + 1                    \r\n" );
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document.write( "    10x + 10 = 3x + 3w + 6                \r\n" );
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document.write( "The standard form equations\r\n" );
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document.write( "    2x -  w = -2,      (3)\r\n" );
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document.write( "    7x - 3w = -4.      (4)\r\n" );
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document.write( "Apply the Elimination method.  For it, multiply equation (3) by 3;  keep equation (4) as is\r\n" );
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document.write( "    6x - 3w = -6,      (3')\r\n" );
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document.write( "    7x - 3w = -4.      (4')\r\n" );
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document.write( "From equation (4'), subtract equation (3').  You will get\r\n" );
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document.write( "    7x - 6x = -4 - (-6),  or  x = 2.\r\n" );
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document.write( "Then from equation (3),  w = 2x + 2 = 2*2 + 2 = 6.\r\n" );
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document.write( "So, the original solution was 6 kg of water and 2 kg of salt,\r\n" );
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document.write( "and the original mass concentration of the solution was  \"2%2F%282%2B6%29\" = \"2%2F8\" = \"1%2F4\" = 25%.    ANSWER\r\n" );
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