document.write( "Question 1036606: Hi !
\n" ); document.write( "I am having difficulties with this problem, we do not get along.\r
\n" ); document.write( "\n" ); document.write( "We have a 20% alcohol solution and a 50% solution. How many pints must be used from each to obtain 8 pints of a 30% solution ?
\n" ); document.write( "Set up and solve using a system of algebraic equation.\r
\n" ); document.write( "\n" ); document.write( "Thank you so much \n" ); document.write( "
Algebra.Com's Answer #651314 by ikleyn(52781)\"\" \"About 
You can put this solution on YOUR website!
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\n" ); document.write( "Hi !
\n" ); document.write( "I am having difficulties with this problem, we do not get along.\r
\n" ); document.write( "\n" ); document.write( "We have a 20% alcohol solution and a 50% solution. How many pints must be used from each to obtain 8 pints of a 30% solution ?
\n" ); document.write( "Set up and solve using a system of algebraic equation.\r
\n" ); document.write( "\n" ); document.write( "Thank you so much
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document.write( "Let n be the number of pints of the 20% alcohol solution needed, and\r\n" );
document.write( "let m be the number of pints of the 50% alcohol solution needed.\r\n" );
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document.write( "Then the total volume equation is \r\n" );
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document.write( "n + m = 8.   (1)\r\n" );
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document.write( "n pints of the 20% alcohol solution contain 0.2n pints of the pure alcohol.\r\n" );
document.write( "m pints of the 50% alcohol solution contain 0.5m pints of the pure alcohol.\r\n" );
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document.write( "In total, the mixt contains 0.2n + 0.5m pints of the pure alcohol.\r\n" );
document.write( "So, the second equation for the alcohol percentage/contents in the mixt is\r\n" );
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document.write( "\"%280.2n+%2B+0.5m%29%2F8\" = 0.3.\r\n" );
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document.write( "You can rewrite the last equation in the form\r\n" );
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document.write( "0.2n + 0.5m = 0.3*8,   or\r\n" );
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document.write( "0.2n + 0.5m = 2.4.     (2)\r\n" );
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document.write( "These two equations, (1) and (2), form the system of two linear algebraic equations in two unknowns, n and m.\r\n" );
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document.write( "There are many ways to solve it. You can use the Substitution method, for example.\r\n" );
document.write( "For it, express x from (1) as  n = 8-m  and substitute it into (2). You will get\r\n" );
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document.write( "0.2*(8-m) + 0.5m = 2.4,\r\n" );
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document.write( "1.6 -0.2m + 0.5m = 2.4,\r\n" );
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document.write( "0.3m = 2.4 - 1.6 = 0.8,\r\n" );
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document.write( "m = \"0.8%2F0.3\" = \"2\"\"2%2F3\" pint.\r\n" );
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document.write( "Then n = 8 - m = \"5\"\"1%2F3\" pint.\r\n" );
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document.write( "Answer.  \"5\"\"1%2F3\" pint of the 20% alcohol solution and  \"2\"\"2%2F3\" pint of the 50% alcohol solution.\r\n" );
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