Question 1162588
.
<pre>

Let W be the volume of water to add, in ounces.


Then the volume of liquid is 980+W with the amount of the pure alcohol of 420 ounces.


The concentration equation is then


    {{{420/(980+W)}}} = 0.42,


Multiply both sides by the denominator to get


    420 = 0.42*(980+W)


Simplify and find W


    420 = 0.42*980 + 0.42W

    W = {{{(420 - 0.42*980)/0.42}}} = 20.


<U>ANSWER</U>.  20 ounces of water to add.
</pre>


Now, &nbsp;when the answer is just obtained, &nbsp;it seems &nbsp;OBVIOUS &nbsp;to you: &nbsp;when you add &nbsp;20 &nbsp;ounces of water to &nbsp;980 &nbsp;ounces 
of the original mixture, &nbsp;you will have &nbsp;1000 &nbsp;ounces of the diluted mixture with &nbsp;420 &nbsp;ounces of the pure alcohol,
which makes the final mixture &nbsp;42% &nbsp;alcohol.


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


It is a standard and typical mixture problem.


In this site, there is a bunch of lessons, &nbsp;covering various types of mixture problems. &nbsp;See introductory lessons

&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>


For dilution problems, similar to the given one, there is a special lesson

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/mixtures/Special-type-mixture-problems-on-DILUTION-adding-water.lesson>Special type mixture problems on DILUTION adding water</A>



Read the lessons and become an expert in solution the mixture word problems.


Also, &nbsp;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 online textbook under the topic "<U>Mixture problems</U>".



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.