SOLUTION: A 2.5 L container has a mixture of 25% alcohol. How many liters of the mixture must be drained out and replaced with pure alcohol in order to obtain a mixture containing 40% alcoho

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Question 1128980: A 2.5 L container has a mixture of 25% alcohol. How many liters of the mixture must be drained out and replaced with pure alcohol in order to obtain a mixture containing 40% alcohol?
Found 4 solutions by ikleyn, josgarithmetic, josmiceli, greenestamps:
Answer by ikleyn(52802)   (Show Source): You can put this solution on YOUR website!
.

Let W be the volume to drain off from 2.5 liters of the original mixture.


Step 1:  Draining.  After draining,  you have 2.5-W liters of the 25% mixture.


Step 2:  Replacing.  Then you add W liters of the pure alcohol (the replacing step).

                     After the replacing,  you have the same total liquid volume of 2.5 liters.


It contains  0.25(2.5-W) + W  of the pure alcohol.


So, your "concentration equation" is


 = 0.4.    (1)


The setup is done and completed.


Now you need to solve your basic equation  (1).


0.25*(2.5-W) + W = 0.4*2.5

0.25*2.5 - 0.25W + W = 0.4*2.5

0.75W = 1 - 0.625

W =  = 0.5.


Answer.  0.5  of a liter of the original mixture should be drained and replaced with the pure alcohol.

-------------------

There is entire bunch of lessons 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 dry substances like coffee beans, nuts, cashew and peanuts
    - Word problems on mixtures for dry substances like candies, dried fruits
    - Word problems on mixtures for dry substances like soil and sand
    - Word problems on mixtures for alloys
    - Typical word problems on mixtures from the archive
    - Advanced mixture problems
    - Advanced mixture problem for three alloys
    - OVERVIEW of lessons on word problems for mixtures
in this site.

A convenient place to quickly observe these lessons from a  "bird flight height"  (a top view)  is the last lesson in the list.

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 josgarithmetic(39620)   (Show Source): You can put this solution on YOUR website!
------
A 2.5 L container has a mixture of 25% alcohol. How many liters of the mixture must be drained out and replaced with pure alcohol in order to obtain a mixture containing 40% alcohol?
------

Drain and replace volume v liters.

Drain first v liters of 25% alcohol and then replace with v liters of the 100% alcohol.


Simplify and solve for v.

Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
Let = liters to be drained out and
replaced with liters of pure alcohol
= liters of alcohol that were removed
-----------------------------------------------------





.5 liters must be drained and replaced with pure alcohol
-------------------
check:




OK

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


You already have three good responses to your question, all of them involving a moderately complicated algebraic equation.

Here is a MUCH faster and easier way to solve a "mixture" problem like this.

(1) You are adding 100% alcohol to 25% alcohol; you want to end up with 40% alcohol.
(2) 40% is 1/5 of the way from 25% to 100%. (40-25 = 15; 100-25 = 75; 15/75 = 1/5)
(3) That means 1/5 of the mixture should be the 100% alcohol that you are adding.

1/5 of the 2.5L capacity of the container is 0.5L.

ANSWER: 0.5L of the 25% alcohol should be drained and replaced with 100% alcohol to get 2.5L of 40% alcohol.

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