SOLUTION: How many gallons of 40% alcohol solution must be mixed with 70% solution to obtain 30 gallons of 52% alcohol solution?

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Question 1151235: How many gallons of 40% alcohol solution must be mixed with 70% solution to obtain 30 gallons of 52% alcohol solution?
Found 3 solutions by josmiceli, greenestamps, josgarithmetic:
Answer by josmiceli(19441)   (Show Source):
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Let = gallons of 40% alcohol needed
= gallons of 70% alcohol needed
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and

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18 gallons of 40% alcohol are needed
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check:

OK

Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!

Here is a very different way for solving problems like this involving a mixture of two ingredients.

If you understand it, it will get you to the answer much faster, and with less effort, than the traditional algebraic method.

(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)

(2) That means 2/5 of the mixture is the 70% ingredient.

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.

Answer by josgarithmetic(39618)   (Show Source):
You can put this solution on YOUR website!
H=70
L=30
M=30
T=52, the target percentage for the mixture
v gallons of H%
M-v gallons of L%

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Substitute the given values and evaluate M-v.