SOLUTION: a 30 quart cooling system is checked and found to be filled with a solution that is 40% antifreeze. The desired strength of the solution is 60% antifreeze. How many quarts of solut

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Question 1017355: a 30 quart cooling system is checked and found to be filled with a solution that is 40% antifreeze. The desired strength of the solution is 60% antifreeze. How many quarts of solution need to be drained and replaced with pure antifreeze to reach the desired strength?
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
40% antifreeze in 30 quarts equals 12 quarts of pure antifreeze.
60% antifreeze in 30 quarts equals 18 quarts of pure antifreeze.

you need to pour out x number of quarts of 40% antifreeze and replace them with x quarts of 100% antifreeze to get a solution that is 30 quarts of 60% antifreeze.

each quart that you replace with 100% antifreeze loses you 40% antifreeze, so you get a net gain of 60% antifreeze for each quart that you replace.

you need 6 quarts of pure antifreeze.
in order to gain 6 quarts of pure antifreeze, you need to add 6/.6 = 10 quarts of 60% antifreeze.

you will then have a solution that is 60% antifreeze.

here's how it works.

you have 30 quarts of 40% antifreeze.
you remove 10 quarts of 40% antifreeze and replace them with 10 quarts of 100% antifreeze.

you are left with 20 quarts of 40% antifreeze and 10 quarts of 100% antifreeze.

the 20 quarts of 40% antifreeze give you .4 * 20 = 8 quarts of pure antifreeze.
add the 10 quarts of pure antifreeze to that and you have a total of 18 quarts of pure antifreeze in a 30 quart solution.

the percent antifreeze is now 18/30 = .6 = 60%.

your solution is that you need to drain 10 quarts of antifreeze and replace them with 10 quarts of pure antifreeze to get 30 quarts of 60% antifreeze.