Question 1169761
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            For many students,  such problems perplex them.


            Surely, the most intriguing part is to setup them correctly.


            Here I propose my version of setup and solution.



<pre>
Let M be the amount of money: the unknown value under the problem's question.


In the basic scenario, the number of students is  {{{M/20}}}.

In the hypothetical scenario  ( " if " ), the number of students is  {{{M/40}}}.


The difference is 5, which gives you this equation

    {{{M/20}}} - {{{M/40}}} = 5.


At this point, the setup is just done and completed.


The solution of the equation is in couple of lines.  Multiply both sides by 40.  You will get

    2M     -  M  = 5*40

         M       = 200.


<U>ANSWER</U>.  The amount of money is 200 dollars.


<U>CHECK</U>.   {{{200/20}}} = 10 students;   {{{200/40}}} = 5 students;   10-5 = 5 students,   which is PRECISELY CORRECT !
</pre>

Solved.


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When you solve it in this way,  &nbsp;you feel  a joy  of  getting mathematically beautiful solution &nbsp;(!)



/\/\/\/\/\/\/\/


If you ask me for what purposes math teachers and textbooks give such problems to students, my answer would be



&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"such problems play very important role teaching students to distinct really beautiful Math problems from routine ones


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;and really nice solutions from all the others."



Therefore I so enthusiastically support and promote such problems at this forum.