Question 1149745
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A solution that is 80% acid and 20% water is mixed with a solution that is 50% acid and 50% water. 
If twice as much 50% acid solution is used as 20% solution, what is the ratio of acid to water in the mixture of the solutions.
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&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;First what I want to say regarding this problem is that it is a &nbsp;<U>PROVOCATION</U> &nbsp;in its purest form.


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Nobody, &nbsp;never and nowhere calls &nbsp;(20% water per 80% acid) &nbsp;as &nbsp;20% &nbsp;solution.


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;It is called 80% solution --- <U>THIS &nbsp;AND &nbsp;ONLY &nbsp;THIS &nbsp;way</U>.


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Therefore, the question formulation &nbsp;MUST &nbsp;BE 


<pre>
            If twice as much 50% acid solution is used as 80% solution, what is the ratio of acid to water in the mixture of the solutions ?
</pre>


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;For this formulation, &nbsp;my solution is as follows.


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(I will produce a solution as simple as possible).



<pre>
Let assume that we use 100 liters of the 80% acid solution.

Then the volume of the 50% acid solution is 200 liters, according to the problem's description.



100 liters of the 80% acid solution contain  0.8*100 = 80 liters of the pure acid.

200 liters of the 50% acid solution contain 0.5*200 = 100 liters of the pure acid.


Thus you have 100+200 = 300 liters of the resulting mixture, containing 80+100 = 180 liters of the pure acid.


Thus the concentration of the resulting mixture is  {{{180/300}}} = {{{3/5}}} = 60%

    and

the ratio under the question is  {{{180/(300-180)}}} = {{{180/120}}} = {{{3/2}}}.     <U>ANSWER</U>
</pre> 

Solved.


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I ask the author of the post do not submit such &nbsp;PROVOCATIVE &nbsp;formulations &nbsp;(!) &nbsp;(!) &nbsp;(!)