Question 1168573
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            Such problems usually go in one of two possible modifications.


            One modification asks about the number of the benches of each of the two types.


            If so, then the approach showed you by other tutor is justified and robust.


            The other modification may ask you about the number of some special type of bunches - about unstained benches,
            for example,  as it is in your case.


            For such modification,  the use of systems of two equations  IS  NOT  justified - - - there is  MORE  SIMPLE,  shorter  and 
            MORE  STRAIGHFORWARD   method.


            I show it below in my solution.



<pre>
Let x be the number of unstained benches.


Then, OBVIOUSLY, the number of stained benches is (21-x) :

    you simply subtract that "x" from the total.


Now you can write the  "<U>total money equation</U>"

    20x + 32*(21-x) = 600  dollars.


    +----------------------------------------------------------------------+
    |    This single equation is EXACTLY what you ask about in your post.  |
    +----------------------------------------------------------------------+


Now, you did not ask to solve it;

    however, I will do it for you to show how simple the steps are.


Simplify this equation

    20x + 32*21 - 32x = 600

    32*21 - 600 = 32x - 20x

     72         = 12x

      x         = {{{72/12}}} = 6.


That's all.  The solution is just completed,

and the <U>ANSWER</U> is  6 unstained benches.
</pre>

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The job is done, &nbsp;and, &nbsp;as you see, &nbsp;I used only one single equation, 
instead of using the system of two equations.


I hope that I answered your question in full.


If you have questions, &nbsp;don't hesitate to post them to me.



Happy learning (!)