Question 1072131
.
You have 10 cups of a cleaning solution that is 10% white vinegar and 90% water. You want the mixture to be 20% white vinegar 
and 80% water. How many cups of white vinegar do you need to add to the mixture?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~


<pre>
Let x be the volume of white vinegar you need to add to the mixture (measured in cups).

Then the amount of the pure vinegar in the mixture will be (10*0.1 + x) cups.

The volume of liquid will be 10 + x.

The concentration equation is

{{{(10*0.1 + x)/(10+x)}}} = 0.2.

Multiply both sides by (10+x) and then simplify. You will get

1 + x = 0.2x + 2,

x - 0.2x = 2 - 1  --->  0.8x = 1  --->  x = {{{1/0.8}} = {{{10/8}}} = 1.25.

<U>Answer</U>.  you need to add 1.25 of a cup of the pure vinegar to the mixture.

<U>Check</U>.  {{{0.1*10 + 1.25)/(10+1.25)}}} = {{{2.25/11.25}}} = 0.2.  Correct !
</pre>

Solved.


The solution by "josgarithmetic is <U>WRONG</U>. 



There is entire bunch of 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 online textbook under the topic "<U>Mixture problems</U".