document.write( "Question 1182238: A man adds 1.6 liters of a 60% antifreeze solution to the water already in his car radiator. When the radiator is filled the solution is 8% antifreeze. How many liters does the radiator hold? (Hint: The water is a 0% antifreeze solution) \n" ); document.write( "

Algebra.Com's Answer #812211 by ikleyn(52946) $\"\"$ $\"About$

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\n" ); document.write( "A man adds 1.6 liters of a 60% antifreeze solution to the water already in his car radiator.
\n" ); document.write( "When the radiator is filled the solution is 8% antifreeze.
\n" ); document.write( "How many liters does the radiator hold? (Hint: The water is a 0% antifreeze solution)
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document.write( "1.6 liters of the 60% antifreeses contains 0.6*1.6 = 0.96 liters of the pure antigreese.\r\n" );
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document.write( "Let x be the added volume of the water.\r\n" );
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document.write( "The added water does not contain antifreese, at all.\r\n" );
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document.write( "So we write an equation, saying that the pur antifreese amount is THE SAME before and after mixing\r\n" );
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document.write( "    0.96 = 0.08*(1.6+x)\r\n" );
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document.write( "It is easy to solve\r\n" );
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document.write( "     = 1.6 + x\r\n" );
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document.write( "    12 = 1.6 + x\r\n" );
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document.write( "    x = 12 - 1.6 = 10.4.\r\n" );
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document.write( "So, 10.4 liters is the added volume of water; the total volume of the liquid in the tank after mixing is 1.6 + 10.4 = 12 liters.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "It can be solved by the other way (MENTAL reasoning without using equations).\r
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document.write( "Originally, there were  0.6*1.6 = 0.96 liters of the pure antifreese in the tank.\r\n" );
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document.write( "After adding water, the amount of the pure antifreese did not change, but the concentration became 0.08.\r\n" );
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document.write( "Hence, the total volume after mixing is   = 12 liters.\r\n" );
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\n" ); document.write( "\n" ); document.write( "It is the same solution as the Algebra solution above, but presented in wording form.\r
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\n" ); document.write( "\n" ); document.write( "To see many other similar (and different) problems of the same type, look into the lesson\r
\n" ); document.write( "\n" ); document.write( " - Special type mixture problems on DILUTION adding water\r
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