David needs a 50% solution of antifreeze and water in his radiator. the radiator currently has a 20% solution of antifreeze and water. if the radiator holds 16 quarts, how much of the 20% solution must be drained and replaced with pure antifreeze to create the desired solution?

Let the amount to be drained and replaced be quarts.

We know that the volume of the radiator is 16 quarts.

We also know that the pure antifreeze in the final solution is . Therefore, the volume of antifreeze in the final solution will be

Thus our equation will be:

This is because the x amount of the 20% solution is removed from 16 quarts and replaced with "pure" antifreeze. And we know that by pure we mean a 100% or 1 antifreeze. Thus, .

Therefore, solving the above equation, we get:

Thus, quarts is the required answer.

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