Question 1107389
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Here is a complete different method for solving mixture problems like this which, if you understand it, can get you to the answers much faster and with far less effort then the traditional algebraic method.<br>
(1) The percentage of the mixture, 17%, is 1/6 of the way from 13% to 37%, the percentages of the two ingredients.  (37-13 = 24; 17-13 = 4; 4/24 = 1/6)
(2) Therefore, 1/6 of the mixture needs to be the 37% juice.<br>
That means 5/6 of the mixture is the 270 gallons of 13% juice, making the ratio of the amounts of the two ingredients 5:1.  Then, since 270 gallons of the 13% juice were used, the amount of 37% juice that was used was 270/5 = 54 gallons.