document.write( "Question 1118139: It is necessary to have a 40% antifreeze solution in the radiator of a certain car. The radiator now has 70 liters of 20% solution. How many liters of this should be drained and replaced with 100% antifreeze to get the desired strength? \n" ); document.write( "

Algebra.Com's Answer #733387 by ikleyn(52786) $\"\"$ $\"About$

You can put this solution on YOUR website!
.\r
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "Let V be the volume to drain off from 70 liters of antifreeze.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Step 1:  Draining.  After draining,  you have 70-V liters of the 20% antifreeze.\r\n" );
document.write( "\r\n" );
document.write( "                    It contains 0.20*(70-V) of pure antifreeze.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Step 2:  Replacing.  Then you add V liters of the pure antifreeze (the replacing step).\r\n" );
document.write( "\r\n" );
document.write( "                     After the replacing,  you have the same total liquid volume of 70 liters.\r\n" );
document.write( "\r\n" );
document.write( "                     It contains 0.20(70-V) + V liters of pure antifreeze.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So, the antifreeze concentration after replacement is  . \r\n" );
document.write( "\r\n" );
document.write( "It is the ratio of the pure antifreeze volume to the total volume.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Therefore, your \"concentration equation\" is\r\n" );
document.write( "\r\n" );
document.write( " = 0.4.    (1)    \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The setup is done and completed.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "To solve the equation (1), multiply both sides by 20. You will get\r\n" );
document.write( "\r\n" );
document.write( "0.20*(70-V) + V= 0.4*70,\r\n" );
document.write( "\r\n" );
document.write( "14 - 0.20V + V= 28,\r\n" );
document.write( "\r\n" );
document.write( "0.8V = 28 - 14 = 14  ====>  V =  = 17.5 liters.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Answer.  17.5 liters of the 20% antifreeze must be drained and replaced by 17.5 liters of pure antifreeze.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Check.    = 0.4.    ! Correct !\r\n" );
document.write( "

\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "-----------------
\n" ); document.write( "There is entire bunch of introductory lessons covering various types of mixture problems\r
\n" ); document.write( "\n" ); document.write( "    - Mixture problems\r
\n" ); document.write( "\n" ); document.write( "    - More Mixture problems\r
\n" ); document.write( "\n" ); document.write( "    - Solving typical word problems on mixtures for solutions \r
\n" ); document.write( "\n" ); document.write( "    - Word problems on mixtures for antifreeze solutions (*)\r
\n" ); document.write( "\n" ); document.write( "    - Word problems on mixtures for alloys \r
\n" ); document.write( "\n" ); document.write( "    - Typical word problems on mixtures from the archive\r
\n" ); document.write( "\n" ); document.write( "in this site.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Read them and become an expert in solution mixture word problems.
\n" ); document.write( "Notice that among these lessons there is one on antifreeze solutions marked by (*).\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Also, you have this free of charge online textbook in ALGEBRA-I in this site\r
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The referred lessons are the part of this textbook in the section \"Word problems\" under the topic \"Mixture problems\".\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Save the link to this online textbook together with its description\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-I
\n" ); document.write( "https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "to your archive and use it when it is needed.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );