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You can set up the appropriate equation for this situation from the problem description.
Let x = the required number of quarts of pure (100%) antifreze, then (20-x) = the required number of quarts of 40% antifreeze solution which, when added together, will give 20 quarts of 50% antifreeze solution. Change the percentages to their decimal equivalents. The equation is:
Simplify and solve for x.
Subtract 8 from both sides of the equation.
Divide both sides by 0.6
= 3 1/3
x = 3 1/3 quarts of pure antifreeze.
20-x = 16 2/3 quarts of 40% antifreeze.