Question 406730
The radiator in a car is filled with a solution of 60% antifreeze and 40% water. The manufacturer of the antifreeze suggests that, for summer driving, optimal cooling of the engine is obtained with only 50% antifreeze. If the capacity of the radiator is 3.6L, how much coolant should be drained and replaced with water to reduce the antifreeze concentration to the recommended level?
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We start with 3.5 liters of liquid

We drain out x liters of the liquid.

That leaves 3.5-x liters of the liquid.

Those 3.5-x liters of the liquid contains 60% antifreeze.

Therefore those 3.5-x liters of the liquid left in the radiator contain
.60(3.5-x) liters of antifreeze.

Now we fill up the radiator with water, and when we do we will have
3.5 liters of liquid, and 50% of those 3.5 liters, or .50(3.5) liters,
of liquid now will be the .60(3.5-x) liters of antifreeze left in the
radiator.

So we set those equal:
   
       .50(3.5) = .60(3.5-x)

Solve that and get 7/12 of a liter or about .58 liters.

Edwin</pre>