document.write( "Question 1132366: A tank holds 80 liters of a chemical solution. Currently, the solution has a strength of 30%. How much of this solution must be DRAINED and REPLACED with a 70% solution to get a strength of 40%? (use only one variable and thanks in advance) \n" ); document.write( "
Algebra.Com's Answer #749421 by ikleyn(52943)\"\" \"About 
You can put this solution on YOUR website!
.
\n" ); document.write( "
\r\n" );
document.write( "\r\n" );
document.write( "Let W be the volume to drain off from 80 liters of solution.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Step 1:  Draining.  After draining,  you have (80-W) liters of the 30% acid solution.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Step 2:  Replacing.  Then you add W liters of the 70% solution (the replacing step).\r\n" );
document.write( "\r\n" );
document.write( "                     After the replacing,  you have the same total liquid volume of 80 liters.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "It contains  0.3*(80-W) + 0.7*W   of pure solvent.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So, your \"concentration equation\" is\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    \"%280.30%2A%2880-W%29+%2B+0.7%2AW%29%2F80\" = 0.4.    (1)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "At this point, the setup is done and completed.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Now you need to solve your basic equation  (1).\r\n" );
document.write( "\r\n" );
document.write( "As the first step, multiply both sides by 80, and then simplify\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    0.30*(80-W) + 0.7*W = 0.4*80\r\n" );
document.write( "\r\n" );
document.write( "    24 - 0.3W + 0.7W = 32\r\n" );
document.write( "\r\n" );
document.write( "    0.4W = 32 - 24 = 8\r\n" );
document.write( "\r\n" );
document.write( "    W = \"8%2F0.4\" = 20.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "ANSWER.  20 liters of the original 30% solution should be drained and replaced by 20 liters of the 70% solutions.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "CHECK.   \"%280.3%2A%2880-20%29+%2B+0.7%2A20%29%2F80\" = 0.4.    ! Precisely correct !\r\n" );
document.write( "
\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "---------------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "There is entire bunch of 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 dry substances like coffee beans, nuts, cashew and peanuts\r
\n" ); document.write( "\n" ); document.write( "    - Word problems on mixtures for dry substances like candies, dried fruits\r
\n" ); document.write( "\n" ); document.write( "    - Word problems on mixtures for dry substances like soil and sand\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( "    - Advanced mixture problems \r
\n" ); document.write( "\n" ); document.write( "    - Advanced mixture problem for three alloys \r
\n" ); document.write( "\n" ); document.write( "    - OVERVIEW of lessons on word problems for mixtures\r
\n" ); document.write( "\n" ); document.write( "in this site.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "A convenient place to quickly observe these lessons from a  \"bird flight height\"  (a top view)  is the last lesson in the list.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Read them and become an expert in solution the mixture word problems.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Specially for \"draining - replacing\" mixture problems see the lesson marked (*) in the list.\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 online textbook 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" );