Question 1149876
.


            In this problem, concentration is measured in grams per milliliter, g/mL.  

            //     Not in grams per grams (!)     It is important (!)     And it is important to understand (!)



&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<U>You can solve it using simple logic</U>.



<pre>
100 ml of the 10% salt solution contain  0.1*100 = 10 grams of dissolved salt.


In order 10 grams of dissolved salt make 8% solution, the volume of the solution must be  {{{10/volume}}} = 0.08, i.e.  volume = {{{10/0.08}}} = 125 mL.


So you need add 125-100 = 25 mL of the sterile water.    <U>ANSWER</U>
</pre>


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<U>Or you can solve it using Algebra</U>.



<pre>
Let W be the volume of the sterile water to add.

Then the total volume is  (100+W) milliliters,  and your equation is


    {{{(0.1*100)/(100+W)}}} = 0.08,


saying that the final concentration is 8%.


Solve it.  First step multiply both sides by (100+W).


    0.1*100 = 0.08(100+W)

    10      = 8 + 0.08W

    10 - 8  = 0.08W

     2      = 0.08*W

    W       = {{{2/0.08}}} = 25.


You get the same <U>ANSWER</U> : 25 mL of the sterile water should be added.
</pre>

Solved (in two ways).


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


It is a typical and standard mixture problem.


There is a bunch of introductory lessons in this site, &nbsp;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>


Read them 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.