Question 1051159
.
a chemist needs 25 liters of a 10% alcohol solution but has only a 25% alcohol solution. 
how many liters each of the 25% solution and water should he mix to make the desired 25 liters of 10% solution?
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<U>Solution 1</U>. One equation in one unknown.


<pre>
Let W be the volume of water in liters to mix with the 25% alcohol.

Then the volume of the 25% alcohol solution is (25-W) liters.

The "alcohol content" equation is 

0.25*(25-W) = 0.1*25,     (1)   

or

6.25 - 0.25W = 2.5  --->  -0.25W = 2.5 - 6.25  --->  -0.25W = 15.

15 liters of water is needed.

<U>Answer</U>.  Mix 25-15 = 10 liters of the 25% alcohol and 15 liters of water, and you will get 25 liters of the 10% alcohol.
</pre>


<U>Solution 2</U>. Two equations in two unknown.


<pre>
Let W be the volume of water in liters to mix with the 25% alcohol.
Let A be the volume of the 50% alcohol to mix.

Then the volume equation is 

A + W = 25             (1)

The "alcohol content" equation is

0.25A = 0.1*25.        (2)

Express A = 25-W from (1) and substitute it into (2). You will get

0.25(25-W) = 0.*25.    (3)

This equation coincides with the equation (1) of the <U>Solution 1</U> above and, hence, has the same solution.

So, in this way you get the same answer.
</pre>

There is entire bunch of the lessons covering various types of mixture problems

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/mixtures/Mixture-problems.lesson>Mixture problems</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/mixtures/More-Mixture-problems.lesson>More Mixture problems</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/mixtures/Solving-typical-mixture-problems.lesson>Solving typical word problems on mixtures for solutions</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/mixtures/Word-problems-on-mixtures-for-antifreeze-solutions.lesson>Word problems on mixtures for antifreeze solutions</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/mixtures/Word-problems-on-mixtures-for-alloys.lesson>Word problems on mixtures for alloys</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/mixtures/Typical-word-problems-on-mixtures-from-the-archive.lesson>Typical word problems on mixtures from the archive</A>

in this site.


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

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-I - YOUR ONLINE TEXTBOOK</A>.


The referred lessons are the part of this textbook in the section "<U>Word problems</U>" under the topic "<U>Mixture problems</U>".


The textbook contains many other solved word problems, as well as many other interesting and useful things.