<PRE><B>Question 1121352</B>
.
&lt;pre&gt;
Let x = &quot;How many grams of pure silver must a silversmith mix&quot;.


Then the total mass is  (100 + x) grams, and the concentration equation is


    {{{(0.55*100 + x)/(100+x)}}} = 0.75.      &lt;&lt;&lt;---===  &lt;U&gt;The ratio of the pure silver mass of the alloy to the total mass&lt;/U&gt;


Simplify and solve step by step


    0.55*100 + x = 0.75*(100 + x)


    0.55*100 + x = 0.75*100 + 0.75x


    x - 0.75x = 75 - 55


    0.25x = 20  ====&gt;  x = {{{20/0.25}}} = 80.


&lt;U&gt;Answer&lt;/U&gt;.  80 grams of pure silver should be mixed.  The total mass of the resulting alloy then is 180 grams.


&lt;U&gt;Check&lt;/U&gt;.   {{{(0.55*100+80)/(100+80)}}} = 0.75     ! Correct !
&lt;/pre&gt;

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It is a standard and typical mixture word problem. 


There is entire bunch of introductory lessons covering various types of mixture problems

&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;- &lt;A HREF=http://www.algebra.com/algebra/homework/word/mixtures/Mixture-problems.lesson&gt;Mixture problems&lt;/A&gt;

&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;- &lt;A HREF=http://www.algebra.com/algebra/homework/word/mixtures/More-Mixture-problems.lesson&gt;More Mixture problems&lt;/A&gt;

&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;- &lt;A HREF=http://www.algebra.com/algebra/homework/word/mixtures/Solving-typical-mixture-problems.lesson&gt;Solving typical word problems on mixtures for solutions&lt;/A&gt; 

&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;- &lt;A HREF=https://www.algebra.com/algebra/homework/word/mixtures/Word-problems-on-mixtures-for-antifreeze-solutions.lesson&gt;Word problems on mixtures for antifreeze solutions&lt;/A&gt; 

&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;- &lt;A HREF=https://www.algebra.com/algebra/homework/word/mixtures/Word-problems-on-mixtures-for-alloys.lesson&gt;Word problems on mixtures for alloys&lt;/A&gt; 

&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;- &lt;A HREF=https://www.algebra.com/algebra/homework/word/mixtures/Typical-word-problems-on-mixtures-from-the-archive.lesson&gt;Typical word problems on mixtures from the archive&lt;/A&gt;

&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;- &lt;A HREF=https://www.algebra.com/algebra/homework/word/mixtures/Advanced-mixture-problems.lesson&gt;Advanced mixture problems&lt;/A&gt; 

&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;- &lt;A HREF=https://www.algebra.com/algebra/homework/word/mixtures/Advanced-mixture-problem-for-three-alloys.lesson&gt;Advanced mixture problem for three alloys&lt;/A&gt; 

in this site.


You will find there ALL TYPICAL mixture problems with different methods of solutions,
explained at different levels of detalization, &amp;nbsp;from very detailed to very short.


Read them and become an expert in solution mixture word problems.


Also, &amp;nbsp;you have this free of charge online textbook in ALGEBRA-I in this site

&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;- &lt;A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson&gt;ALGEBRA-I - YOUR ONLINE TEXTBOOK&lt;/A&gt;.


The referred lessons are the part of this textbook in the section &quot;&lt;U&gt;Word problems&lt;/U&gt;&quot; under the topic &quot;&lt;U&gt;Mixture problems&lt;/U&gt;&quot;.



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.



</PRE>