SOLUTION: How many gallons of a 90​% antifreeze solution must be mixed with 80 gallons of 30​% antifreeze to get a mixture that is 80​% ​antifreeze?
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Question 1094741: How many gallons of a 90% antifreeze solution must be mixed with 80 gallons of 30% antifreeze to get a mixture that is 80% antifreeze? Answer by greenestamps(13200) (Show Source):
(1) Look to see how far (or close) the percentage of the mixture is to the percentages of the two ingredients:
The percentage of the mixture, 80%, is "5 times as close" to 90% as it is to 30%. That means there must be 5 times as much of the 90% ingredient as the 30% ingredient. Since there are 80 gallons of the 30% antifreeze, the number of gallons of 90% antifreeze needed is 5*80 = 400.
If you want to use the slow traditional algebraic solution method...
let x = liters of 90% antifreeze
80 = liters of 30% antifreeze
The total mixture is (80+x) liters; the amount of antifreeze is 30% of the 80, plus 90% of the x. You want the antifreeze to be 80% of the total mixture, so
You need to use 400 gallons of the 90% antifreeze.
