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Question 1159861: how much water should be added to 20 liters of an 18% acid solution to reduce the concentration to 15% acid
Found 3 solutions by ikleyn, MathTherapy, greenestamps:
Answer by ikleyn(52887)   (Show Source):
You can put this solution on YOUR website! .
The pure acid amount in 20 liters of the 18% solution is 0.18*20 = 3.6 liters.
To have 15% concentration, the total volume V should be
 = 0.15, or V =  = 24 liters.
Hence, 24 - 20 = 4 liters of water should be added. ANSWER
Solved.
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The problem can be solved by Different ways.
For introductory lessons covering various types of mixture word problems see
- Mixture problems
- More Mixture problems
- Solving typical word problems on mixtures for solutions
- Typical word problems on mixtures from the archive
in this site.
You will find there ALL TYPICAL mixture problems with different methods of solutions,
explained at different levels of detalization, from very detailed to very short.
Read them and become an expert in solution mixture word problems.
Also, you have this free of charge online textbook in ALGEBRA-I in this site
- ALGEBRA-I - YOUR ONLINE TEXTBOOK.
The referred lessons are the part of this textbook in the section "Word problems" under the topic "Mixture problems".
Save the link to this online textbook together with its description
Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson
to your archive and use it when it is needed.
Answer by MathTherapy(10557)  (Show Source):
You can put this solution on YOUR website!
how much water should be added to 20 liters of an 18% acid solution to reduce the concentration to 15% acid
Let amount of water to add, be W
Water + water = Water, OR
.82(20) + 1(W) = .85(20 + W)
16.4 + W = 17 + .85W
W - .85W = 17 - 16.4
.15W = .6
Water to add, or 
Answer by greenestamps(13209)  (Show Source):
You can put this solution on YOUR website!
The responses from tutors @MathTherapy and @ikleyn both show good methods for solving this problem.
I will show you a third way. It is not in any way better than either of the methods they showed -- it is simply an alternative. Study all three methods and determine which one "works" best for you.
(1) You are starting with 18% acid and adding 0% acid, stopping when you get to 15%.
(2) 15 is 1/6 of the way from 18 to 0. (18 to 0 is a difference of 18; 18 to 15 is a difference of 3; 3/18 = 1/6.
(3) Since you went 1/6 of the way from 18 towards 0, 1/6 of the mixture is what you added.
(4) So the 20 liters you started with was 5/6 of the mixture; that means the 1/6 of the mixture that is the added water is 20/5 = 4 liters.
All the words of explanation make this sound like a long process, but it is not. Without the words, here is the complete solution:
18-0 = 18; 18-15 = 3; 3/18 = 1/6
1-1/6 = 5/6
5/6 is 20 liters, so 1/6 is 4 liters
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