SOLUTION: how many liters each of a 15% acid solution and a 25% acid solution must be used to produce 80 liters of a 20% acid solution

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Question 746137: how many liters each of a 15% acid solution and a 25% acid solution must be used to produce 80 liters of a 20% acid solution
Found 3 solutions by josgarithmetic, amalm06, Alan3354:
Answer by josgarithmetic(39617) About Me  (Show Source):
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The quick guess is 40 liters of each, given numbers like those.

The solving process:
u and v for volumes to use
%2815u%2B25v%29%2F80=20 and u%2Bv=80

15u%2B25v=1600
3u%2B5v=320
working from volume sum equation, v=80-u, so substitute.
3u%2B5%2880-u%29=320
3u%2B400-5u=320
-2u=320-400
2u=400-320
2u=80
highlight%28u=40%29, ..... See what I mean?

Answer by amalm06(224) About Me  (Show Source):
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The problem can be solved using the method of alligation.

Let S1 denote the 15% acid solution.

Let S2 denote the 25% acid solution.

Then 25-20=5 and 20-15=5

Therefore, the ratio of S1/S2=1/1

Since there are 2 parts of mixture for every 1 part of S1 (WLOG), we have the following relation:

S1=(1/2)(80)= 40 L (Answer)

S2=80-40= 40 L (Answer)

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
how many liters each of a 15% acid solution and a 25% acid solution must be used to produce 80 liters of a 20% acid solution
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20 is the average of 15 & 25 --> equal amounts