Question 1172281
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The "drained off..." and "replaced by..." language is only used to confuse you.<br>
Essentially the problem is just mixing 20% alcohol and 100% alcohol to get 30% alcohol.<br>
For a quick and easy non-algebraic method for solving the problem, note that you are starting with a 20% alcohol solution and adding 100% alcohol, stopping when you get to 30% alcohol.<br>
With that way of thinking of the problem, observe that 30% is 1/8 of the way from 20% to 100% (20 to 30 is 10; 20 to 100 is 80; 10/80 = 1/8); that means 1/8 of the final mixture is the added 100% alcohol.<br>
Since the capacity of the radiator is 18 quarts, the amount of 100% alcohol in the mixture is 18/8 = 2.25 quarts.<br>
ANSWER: 2.25 quarts of the original solution must be drained off and replaced by 100% alcohol to obtain 18 quarts of 30% alcohol.<br>