# SOLUTION: An automobile cooling system currently has 20 quarts of a 35% antifreeze solution. The manufacturer recommends the systme be filled with a 50% antifreeze solution. How much of th

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 Click here to see ALL problems on Mixture Word Problems Question 25177: An automobile cooling system currently has 20 quarts of a 35% antifreeze solution. The manufacturer recommends the systme be filled with a 50% antifreeze solution. How much of the 35% soulution must be drained off so that when replaced by pure antifreeze, the system contains the recommended 50% solution?Answer by AnlytcPhil(1277)   (Show Source): You can put this solution on YOUR website!```An automobile cooling system currently has 20 quarts of a 35% antifreeze solution. The manufacturer recommends the systme be filled with a 50% antifreeze solution. How much of the 35% soulution must be drained off so that when replaced by pure antifreeze, the system contains the recommended 50% solution? Let x = amount to be drained off After we drain off x quarts we have left 20-x quarts of 35% solution. The number of quarts of pure antifreeze contained in the 20-x quarts that are left in the radiator after draining is .35(20-x) The number of quarts of pure antifreeze contained in the x quarts that we are going to add is x quarts, because it is 100% antifreeze The total number of quarts of pure antifreeze contained in the full radiator after we add the x quarts of pure antifreeze is .35(20-x) + x Also the number of quarts of pure antifreeze that must be contained in the full radiator after we add the pure antifreeze must be 50% of 20 or .50(20) or 10 quarts So .35(20-x) + x must equal 10 .35(20-x) + x = 10 solve that and get x = 60/13 or 4 8/13 quarts Edwin AnlytcPhil@aol.com```