document.write( "Question 1207753: The cooling system of a certain foreign-made car has a capacity of 15 liters. If the system is filled with a mixture that is 40% antifreeze, how much of this mixture should be drained and replaced by pure antifreeze so that the system is filled with a solution that is 60% antifreeze?\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Let me see.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Mixture 1 + mixture 2 = total mixture \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "15(0.40) + x = 0.60(x + 15)\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Is this the correct set up? \n" ); document.write( "
Algebra.Com's Answer #845804 by ikleyn(52781)\"\" \"About 
You can put this solution on YOUR website!
.
\n" ); document.write( "The cooling system of a certain foreign-made car has a capacity of 15 liters.
\n" ); document.write( "If the system is filled with a mixture that is 40% antifreeze, how much of this mixture should be drained
\n" ); document.write( "and replaced by pure antifreeze so that the system is filled with a solution that is 60% antifreeze?\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Let me see.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Mixture 1 + mixture 2 = total mixture \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "15(0.40) + x = 0.60(x + 15)\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Is this the correct set up?
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Your setup equation is  INCORRECT.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "This problem is a standard and typical mixture problem.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "To see many similar problems solved with detailed explanations,  look into the lessons\r
\n" ); document.write( "\n" ); document.write( "    - Word problems on mixtures for antifreeze solutions \r
\n" ); document.write( "\n" ); document.write( "in this site.     Learn the subject from there.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "/\/\/\/\/\/\/\/\/\/\/\/\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "        Here I will show you very uncommon method of solution, \r
\n" ); document.write( "\n" ); document.write( "        which allows to solve the problem practically  MENTALLY.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "
\r\n" );
document.write( "The amount of the pure antifreeze in 15 liters of the 40% mixture \r\n" );
document.write( "is 0.4*15 = 6 liters.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The amount of the pure antifreeze in 15 liters of the 60% mixture \r\n" );
document.write( "is 0.6*15 = 9 liters.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So, the original mixture contained 6 liters of the pure antifreeze;\r\n" );
document.write( "the final mixture contains 9 liters of the pure antifreeze.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Now, Let V be the volume of the mixture to replace.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "When we drain V liters of the 40% mixture, 0.4*V liters of the pure antifreeze go out.\r\n" );
document.write( "We replace it with V liters of the pure antifreeze.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So, V should be 3 liters more than 0.4V, which means\r\n" );
document.write( "\r\n" );
document.write( "    V - 0.4V = 3,  or  0.6V = 3,  hence  V = \"3%2F0.6\" = 5 liters.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "At this point, the solution is complete, and we get the \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "ANSWER.  5 liters of the of the original 40% mixture should be drained \r\n" );
document.write( "\r\n" );
document.write( "         and replaced by 5 liters of pure antifreeze.\r\n" );
document.write( "
\r
\n" ); document.write( "\n" ); document.write( "Solved in full and explained completely.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "------------------\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Re-phrasing O'Henry, the famous American writer,\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "        The blind begin to walk and the dumb begin to see
\n" ); document.write( "        when they receive such beautiful solutions to their problems.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "There is nothing here except a mind game.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );