document.write( "Question 1147529: An engine has a 4.4 litre capacity cooling system. If the most ideal solution of antifreeze for this engine is a 62.1 % solution (a mix of 62.1 % pure antifreeze and 37.9 % water). How much pure antifreeze (in litres) must be combined with a 31.4 % solution to achieve 4.4 litres of the ideal solution? \n" ); document.write( "
Algebra.Com's Answer #768866 by Theo(13342)![]() ![]() You can put this solution on YOUR website! capacity of the cooling system is 4.4 liters. \n" ); document.write( "most ideal solution is 62.1% pure antifreeze. \n" ); document.write( "you have x liters of a 31.4% solution. \n" ); document.write( "you want to know how many liters of pure antifreeze you need to add to this to get 4.4 liters of 62.1% solution. \n" ); document.write( "let y = the number of liters of pure antifreeze (100% antifreeze). \n" ); document.write( "your equations are: \n" ); document.write( "x + y = 4.4 \n" ); document.write( ".314 * x + y = .621 * 4.4 \n" ); document.write( "multiply both sides of the first equation by .314 and leave the second equation as is (after simplification) to get; \n" ); document.write( ".314 * x + .314 * y = 1.3816 \n" ); document.write( ".314 * x + y = 2.7324 \n" ); document.write( "subtract the first equation from the second to get: \n" ); document.write( ".686 * y = 1.3508 \n" ); document.write( "solve for y to get: \n" ); document.write( "y = 1.3508 /.686 = 1.96909621. \n" ); document.write( "since x + y = 4.4, then x must be equal to 4.4 minus y = 2.43090379. \n" ); document.write( "confirm by replacing x and y with those values in the two original equations to get: \n" ); document.write( "2.43090379 + 1.96909621 = 4.4 \n" ); document.write( ".314 * 2.43090379 + 1.96909621 = 2.7324. \n" ); document.write( "since .621 * 4.4 = 2.7324, both original equations are correct when x and y are replaced with their respective values, as shown below: \n" ); document.write( "x = 2.43090379 \n" ); document.write( "y = 1.96909621 \n" ); document.write( "you need to add 2.43090379 liters of 31.4% solution with 1.96909621 liters of pure antifreeze to get 4.4 liters of 62.1% solution. \n" ); document.write( "the amount of pure antifreeze is .314 * 2.43090379 + 1.96909621 = 2.7324 \n" ); document.write( "2.7324 / 4.4 = .621 * 100 = 62.1%.\r \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " |