document.write( "Question 275795: Beth wants to make 11.6 fl. oz. of a 45% acid solution by mixing together a 22% acid solution and a 80% acid solution. How much of each solution must she use? \n" ); document.write( "

Algebra.Com's Answer #854138 by ikleyn(53742) $\"\"$ $\"About$

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\n" ); document.write( "Beth wants to make 11.6 fl. oz. of a 45% acid solution by mixing together a 22% acid solution and a 80% acid solution.
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\n" ); document.write( "\n" ); document.write( " Calculations in the post by @mananth are incorrect, leading to wrong answer.\r
\n" ); document.write( "\n" ); document.write( " I came to bring a correct solution.\r
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document.write( "Let x be the volume of the 80% solution, in oz.\r\n" );
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document.write( "Then the volume of the 22% solution is  (11.6-x) oz.\r\n" );
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document.write( "The balance equation is\r\n" );
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document.write( "    0.8x + 0.22(11.6-x) = 0.45*11.6.    (1)\r\n" );
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document.write( "It says that the combined mass of pure acid in ingredients (left side) \r\n" );
document.write( "is the same as the mass of pure acid in the mixture (right side).\r\n" );
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document.write( "Simplify and find 'x'\r\n" );
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document.write( "    0.8x + 0.22*11.6 - 0.22x = 0.45*11.6,\r\n" );
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document.write( "    0.8x - 0.22x = 0.45*11.6 - 0.22*11.6\r\n" );
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document.write( "        0.58x    =        2.668\r\n" );
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document.write( "            x    =        2.668/0.58 = 4.6.\r\n" );
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document.write( "ANSWER.  4.6 oz of the 80% solution is needed and  (11.6-4.6) = 7 oz of the 22% solution.\r\n" );
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document.write( "CHECK.   Let's check the final solution for its concentration   = 0.45,\r\n" );
document.write( "         which is precisely correct.\r\n" );
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