document.write( "Question 1088264: Solve the following problem by writing a system of linear equation
\n" ); document.write( "A chemist has two alcohol solutions. One is 2% and the other is 6%. She wants to make 60L of a 5% solution. How much of each solutions must she use? \n" ); document.write( "
Algebra.Com's Answer #702512 by ikleyn(52858)\"\" \"About 
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document.write( "Let x and y be the volumes (in liters, L) to be mixed.\r\n" );
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document.write( "Then one equation is \"the volume\" equation \r\n" );
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document.write( "x + y = 60    (liters)     (1)\r\n" );
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document.write( "for the total volume.\r\n" );
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document.write( "The amount of \"x\" liters of the 2% solution contains 0.02x liters of pure alcohol.\r\n" );
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document.write( "The amount of \"y\" liters of the 6% solution contains 0.06y liters of pure alcohol.\r\n" );
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document.write( "Thus the mixture contains  0.02x + 0.06y liters of pure alcohol.\r\n" );
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document.write( "From the other side, the mixture contains 0.05*60 liters of pure alcohol.\r\n" );
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document.write( "It gives you the second equation, \"pure alcohol contents equation\"\r\n" );
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document.write( "0.02x + 0.06y = 0.05*60   (liters of pure alcohol)   (2)\r\n" );
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document.write( "Combining equations (1) and (2), you have this system of two linear equations for two unknowns\r\n" );
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document.write( "    x +     y = 60,     (3)\r\n" );
document.write( "0.02x + 0.06y =  3.     (4)\r\n" );
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document.write( "Multiply equation (4) by 100 (both sides). You will get an equivalent system in the form\r\n" );
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document.write( " x +  y =  60,          (5)\r\n" );
document.write( "2x + 6y = 300           (6)\r\n" );
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document.write( "To solve it, express x = 60 - y from (5) and substitute into (6) replacing x. You will get\r\n" );
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document.write( "2(60-y) + 6y = 300,\r\n" );
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document.write( "120 - 2y + 6y = 300,\r\n" );
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document.write( "4y = 300 - 120   ====>  4y = 180  ====>  y = \"180%2F4\" = 45.\r\n" );
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document.write( "Answer.  45 liters of the 6% alcohol solution must be mixed with 60-45 = 15 liters of the 2% alcohol solution.\r\n" );
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\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 problem for three alloys \r
\n" ); document.write( "\n" ); document.write( "    - OVERVIEW of lessons on word problems for mixtures\r
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\n" ); document.write( "\n" ); document.write( "Read them and become an expert in solution the 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 online textbook under the topic \"Mixture problems\n" ); document.write( "
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