Question 1151235
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Here is a very different way for solving problems like this involving a mixture of two ingredients.<br>
If you understand it, it will get you to the answer much faster, and with less effort, than the traditional algebraic method.<br>
(1) 52% is 2/5 of the way from 40% to 70%.  (40 to 70 is 30; 40 to 52 is 12; 12/30 = 2/5)<br>
(2) That means 2/5 of the mixture is the 70% ingredient.<br>
ANSWER:
2/5 of 30 gallons, or 12 gallons, of the 70% solution;
3/5 of 30 gallons, or 18 gallons, of the 40% solution.<br>