document.write( "Question 335003: I need to translate this problem into a pair of linear equations in two variables. How many liters of a 40%-alcohol solution must be mixed with 10 liters of a solution that is 80% alcohol to get a solution that is 60% alcohol? Can anyone please help me?
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Algebra.Com's Answer #240179 by nyc_function(2741)![]() ![]() You can put this solution on YOUR website! You get two equations, one based on total volume, and one based on the mix:\r \n" ); document.write( "\n" ); document.write( "x + 10 = y\r \n" ); document.write( "\n" ); document.write( "x(0.4) + 10(0.8) = y(0.6)\r \n" ); document.write( "\n" ); document.write( "Substitute the first equation for \"y\" into the second equation and solve for \"x\":\r \n" ); document.write( "\n" ); document.write( "x(0.4) + 10(0.8) = (x + 10)(0.6)\r \n" ); document.write( "\n" ); document.write( "x(0.4) + 8 = x(0.6) + 6\r \n" ); document.write( "\n" ); document.write( "x(0.4) - x(0.6) = 6 - 8\r \n" ); document.write( "\n" ); document.write( "x(-0.2) = -2\r \n" ); document.write( "\n" ); document.write( "x = -2/-0.2 = 10\r \n" ); document.write( "\n" ); document.write( "Therefore, y = 20.\r \n" ); document.write( "\n" ); document.write( "10 liters of a 40% alcohol solution must be mixed with 10 liters of a 80% alcohol solution to get a 20 liters of a 60% alcohol solution. \n" ); document.write( " \n" ); document.write( " |