document.write( "Question 1175706: A lab technician needs to make 12 liters of 45% alcohol. How much of 40% alcohol and 60% alcohol must he mix to produce this? \n" ); document.write( "

Algebra.Com's Answer #801406 by ikleyn(52787) $\"\"$ $\"About$

You can put this solution on YOUR website!
.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " Both the solution and the answer by @josgarithmetic are INCORRECT.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " I came to bring a correct solution.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "You mix x liters of the 40% alcohol solution and (12-x) liters of the 60% alcohol solution.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Under this approach, the total volume of 12 liters of the resulting mixture is just provided,\r\n" );
document.write( "\r\n" );
document.write( "and all you need to care about is to provide the requested concentration of 45% for the mixture.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So, you write this equation for the concentration\r\n" );
document.write( "\r\n" );
document.write( "     = 0.45,    (1)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "or, which is the same\r\n" );
document.write( "\r\n" );
document.write( "    0.4x + 0.6*(12-x) = 0.45*12       (2)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "From this equation\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    x =  = 9 liters.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "ANSWER.  9 liters of the 40% solution  and  the rest, (12-9) = 3 liters of the 60% solution.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "CHECK.    = 0.45 = 45%  final concentration   ! 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( "It is a standard and typical mixture problem.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "For introductory lessons covering various types of mixture word problems see\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( "    - 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( "You will find there ALL TYPICAL mixture problems with different methods of solutions,
\n" ); document.write( "explained at different levels of detalization, from very detailed to very short.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Read them and become an expert in solution mixture word problems.\r
\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" ); document.write( "

\n" );