SOLUTION: 10 gallons of a 15.0% alcohol solution are to be mixed with a 28.0% alcohol solution to make a 20.0% alcohol solution. How many gallons of a 28.0% alcohol must be used? How many ga

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Question 433981: 10 gallons of a 15.0% alcohol solution are to be mixed with a 28.0% alcohol solution to make a 20.0% alcohol solution. How many gallons of a 28.0% alcohol must be used? How many gallons of a 20.0% alcohol solution are made?
Found 3 solutions by mananth, ikleyn, greenestamps:
Answer by mananth(16949)   (Show Source):
You can put this solution on YOUR website!
------ Percent ---------------- quantity
Alcohol 15 ----------------10
Alcohol II 28----------------x
Total 20 ----------------10+x

15*10+28*x=20(10+x)
150+28x =200+20 x
28 x - 20 x = 200 - 150
8x=50
/8
x=6.25 gallons 28% Alcohol II
Balance 13.75 gallons 15% alcohol

Answer by ikleyn(53418)   (Show Source):
You can put this solution on YOUR website!
.
10 gallons of a 15.0% alcohol solution are to be mixed with a 28.0% alcohol solution to make a 20.0% alcohol solution.
(a) How many gallons of a 28.0% alcohol must be used?
(b) How many gallons of a 20.0% alcohol solution are made?
~~~~~~~~~~~~~~~~~~~~~~~~~~~

       In the post by @mananth, his answer to question (a) is correct,
       but his answer to question (b) is not correct and should be fixed.
       So, I place below the solution with modified/corrected part for question (b).

------ Percent ---------------- quantity
Alcohol 15 ----------------10
Alcohol II 28----------------x
Total 20 ----------------10+x

15*10+28*x=20(10+x)
150+28x =200+20 x
28 x - 20 x = 200 - 150
8x=50
/8

x=6.25 gallons 28% Alcohol II must be used.                 <<<---=== ANSWER to q.  (a)

10+x = 16.25 gallons of the 20% alcohol are made.         <<<---=== ANSWER to q.  (b)

Answer by greenestamps(13258)   (Show Source):
You can put this solution on YOUR website!

The ratio in which the two alcohol solutions must be mixed is exactly determined by where the 20% of the mixture lies between the 15% and 28% of the two ingredients.

The difference between 15 and 20 is 5; the difference between 20 and 28 is 8.

So the two ingredients must be mixed in the ratio 5:8. Note that since 20% is closer to 15% than it is to 28%, the larger portion must be the 15% alcohol solution.

Solve the problem using a proportion, given that we are using 10 gallons of the 15% alcohol.

ANSWERS:
(1) 6.25 gallons of the 28% alcohol should be used
(2) the mixture will be 10+6.25 = 16.25 gallons