Question 1017355
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.