A laboratory needs to prepare 560 liters of an alcohol solution that is at least 32% alcohol by volume by mixing together a 20% alcohol solution with a 45% alcohol solution.
The 45% solution is delivered only in sealed 8-liter barrels, and the laboratory must use a whole number of these barrels (barrels cannot be partially emptied or refilled).
What is the minimum number of 8-liter barrels of the 45% solution that the laboratory must use?