document.write( "Question 1103833: A chemist has three different acid solutions. The first acid solution contains 15% acid, the second contains 30% acid, and the third contains 75% acid. He wants to use all three solutions to obtain a mixture of 216 liter containing 25% acid, using 2 times as much of the 75% solution as the 30% solution. How many liters of each solution should be used? \n" ); document.write( "
Algebra.Com's Answer #718528 by ikleyn(52797)\"\" \"About 
You can put this solution on YOUR website!
.
\n" ); document.write( "
\r\n" );
document.write( "Let x = the volume of the 15% acid (in liters) and \r\n" );
document.write( "\r\n" );
document.write( "let y = the volume of the 30% acid.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Then the volume of the 75% acid is 2y liters.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Then your equations are\r\n" );
document.write( "\r\n" );
document.write( "    x +    y +       2y = 216,         (1)     (total volume)\r\n" );
document.write( "0.15x + 0.3y + 0.75*(2y) = 0.25*216    (2)    (pure acid volume)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Simplify:\r\n" );
document.write( "\r\n" );
document.write( "    x +   3y = 216,                    (3)\r\n" );
document.write( "0.15x + 1.8y =  54.                    (4)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Simplify one more time by multiplying eq(4) by 100 (both sides)\r\n" );
document.write( "\r\n" );
document.write( "    x +   3y =  216,                   (5)\r\n" );
document.write( "  15x + 180y = 5400.                   (6)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Now multiply eq(5) by 15 (both sides). The modified system is\r\n" );
document.write( "\r\n" );
document.write( "  15x +  45y = 3240,                   (7)\r\n" );
document.write( "  15x + 180y = 5400.                   (8)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Next subtract eq(7) from eq(8).  The terms \"15x\" will cancel each other, \r\n" );
document.write( "and you will get a single equation for only one unknown \"y\".    (It is how the Elimination method works).\r\n" );
document.write( "\r\n" );
document.write( "  180y - 45y = 5400 - 3240,\r\n" );
document.write( "\r\n" );
document.write( "  135y = 2160  ====>  y = \"2160%2F135\" = 16.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Answer.  16 liters of the 30% solution,  16*2 = 32 of the 75% solution and the rest 216-(16+32) = 168 liters of the 15% solution.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Check.  0.3*16 + 0.75*32 + 0.15*168 = 54 liters of pure acid;\r\n" );
document.write( "\r\n" );
document.write( "        0.25*216 = 54 liters of pure acid.   ! Correct !\r\n" );
document.write( "
\r
\n" ); document.write( "\n" ); document.write( "Solved.\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( "    - Advanced mixture problems \r
\n" ); document.write( "\n" ); document.write( "    - Advanced mixture problem for three alloys \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" );