SOLUTION: How many liters of water should be added to a 25% antifreeze to obtain 30 liters of a 20% solution could someone please explain how to work this problem out

Question 1144522: How many liters of water should be added to a 25% antifreeze to obtain 30 liters
of a 20% solution
could someone please explain how to work this problem out
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52802)   (Show Source): You can put this solution on YOUR website!
.

Let x be the volume of the original 25% mixture to add water to it. Then the amount of the pure antifreeze in it is 0.25*x liters. The amount of the pure antifreeze in the final 30 liters of the 20% solution (after adding water) is 0.2*30 = 6 liters and it is with no change: 0.25x = 6 liters. Hence, x = = 24 liters. Thus 24 liters of the original 25% solution should be use, and 6 = 30-24 liters of the water should be added. ANSWER

Solved.

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There is a bunch of introductory lessons in this site, covering various types of mixture problems
    - Mixture problems
    - More Mixture problems
    - Solving typical word problems on mixtures for solutions
    - Word problems on mixtures for antifreeze solutions
    - Word problems on mixtures for alloys
    - Typical word problems on mixtures from the archive

Read them and become an expert in solution the 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 online textbook 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 greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

Tutor @ikleyn has provided a response with a detailed algebraic solution, along with links to resources where you can find many other examples of this method for solving this kind of problem.

Here is a non-algebraic solution method which, if you understand it, will get you to the answer to problems like this much faster, and with far less effort, than the formal algebraic method.

Here is the solution using this method for your example.

(1) You are starting with 25% antifreeze solution and adding 0% antifreeze solution (water) to get a 20% antifreeze solution.

(2) Look where 20 lies in relation to the 25 and the 0. Looking at the three numbers on a number line can help: 25, 20, and 0. You should see that 20 is 1/5 of the way from 25 to 0.

(3) That means 1/5 of the mixture should be the water you are adding.

Since the total mixture is to be 30 liters, the amount of water to be used is 30*(1/5) = 6 liters.
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