Question 1156558
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Tutor @ikleyn solves the problem by the traditional algebraic method, using two equations and two unknowns.  This is a good example of how to use algebra to solve problems; you should understand it.<br>
Tutor @josgarithmetic shows how to solve the problem using his/her favorite formula for solving mixture problems, involving a whole bunch of variables.  If you like to memorize ugly formulas (generally without understanding WHERE those formulas come from) then you can use that method.<br>
But if a formal algebraic solution is not required, here is a way you can solve the problem mentally in a few seconds:<br>
(1) 30% is "twice as close to 20% as it is to 50%".  (to help you see this, picture the three percentages 20, 30, and 50 on a number line....)
(2) Therefore, the mixture must contain twice as much of the 20% alcohol as it does the 50% alcohol.<br>
9 gallons total, with twice as much 20% alcohol as 50% alcohol means 6 gallons of 20% and 3 gallons of 50%.<br>