document.write( "Question 1091275: One hundred liters of a 50% solution of a chemical mixture is obtained by mixing a 60% solution with a 20% solution. Using a system of linear equations determine how many liters of each solution are required to obtain the 50% mixture. Solve the system using matrices. \n" ); document.write( "

Algebra.Com's Answer #705663 by ikleyn(52787) $\"\"$ $\"About$

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document.write( "Let x be the volume of the 20% solution,\r\n" );
document.write( "    y be the volume of the 60% solution.\r\n" );
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document.write( "Your system of equations is\r\n" );
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document.write( "   x +     y = 100,        (1)     (account for the volume)\r\n" );
document.write( "0.2x + 0.6*y = 0.5*100     (2)     (account for the pure solvent volume)\r\n" );
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document.write( "You can rewrite it equivalently in the form\r\n" );
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document.write( "   x +     y = 100,        (1')     (account for the volume)\r\n" );
document.write( "0.2x + 0.6*y =  50.        (2')     (account for the pure solvent volume)\r\n" );
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document.write( "The system (1'),(2') is the standard form of equations for the mixture word problems.\r\n" );
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document.write( "You can solve it by applying any appropriate method.\r\n" );
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\n" ); document.write( "\n" ); document.write( "There is a bunch of introductory lessons in this site 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
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\n" ); document.write( "\n" ); document.write( "Read them and become an expert in solution mixture word problems.\r
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\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
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\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
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