document.write( "Question 1039181: A 10-quart radiator contains a 30% antifreeze solution. How much of the solution needs to be drained out and replaced with pure antifreeze in order to raise the solution to 65% antifreeze? \n" ); document.write( "

Algebra.Com's Answer #653943 by ikleyn(52788) $\"\"$ $\"About$

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\n" ); document.write( "A 10-quart radiator contains a 30% antifreeze solution. How much of the solution needs to be drained out and replaced
\n" ); document.write( "with pure antifreeze in order to raise the solution to 65% antifreeze?
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document.write( "Let \"x\" be (an unknown) volume of the 30% antifreeze solution which need to be drained out and replaced, \r\n" );
document.write( "in accordance with the condition.\r\n" );
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document.write( "After draining, you will have (10-x) quarts of the antifreeze solution in the radiator \r\n" );
document.write( "(assuming that initially the radiator was full and contained 10 quarts of the solution).\r\n" );
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document.write( "The amount of the pure antifreeze in the (10-x) quarts of the 30% solution is 0.3*(10-x).\r\n" );
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document.write( "After replacing of \"x\" quarts by the pure antifreeze by \"x\" quarts of the pure antifreeze \r\n" );
document.write( "the amount of the pure antifreeze in the radiator is  0.3*(10-x) + x quarts.\r\n" );
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document.write( "To get the antifreeze concentration of 65%, the volume \"x\" should satisfy the equation\r\n" );
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document.write( " = .   (1)\r\n" );
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document.write( "First step to solve this equation is to multiply both sides by 10 to rid of the denominator. You will get\r\n" );
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document.write( "0.3(10-x) + x = 6.5,   or\r\n" );
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document.write( "3 - 0.3x + x = 6.5  --->  0.7x = 6.5 - 3  --->  0.7x = 3.5  --->  x = 5.\r\n" );
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document.write( "Answer.  The amount of the 65% antifreeze solution that needs to be drained and replaced by the pure antifreeze is 5 quarts.\r\n" );
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