Question 1181027
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I just solved this problem under this link


<A HREF=https://www.algebra.com/algebra/homework/coordinate/word/Linear_Equations_And_Systems_Word_Problems.faq.question.1181026.html>https://www.algebra.com/algebra/homework/coordinate/word/Linear_Equations_And_Systems_Word_Problems.faq.question.1181026.html</A>


https://www.algebra.com/algebra/homework/coordinate/word/Linear_Equations_And_Systems_Word_Problems.faq.question.1181026.html



but the visitor asks "to show a step by step solution on how you solved the problem".



So, I will copy-paste the previous solution and then add couple of words after that.



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<pre>
Two governing inequalities are


      m +   g >=   3     (1)

    20m + 25g <= 100     (2)


3 (three) possible solutions are (for example)


    3m,0g

    4m,0g

    1m,3g
</pre>

To get these solutions, I applied "trial and error" method:  I guessed the possible numbers/(pairs) and then

mentally checked them in my mind.



For example, 


<pre>
    - for the 1st pair, I see that 3 + 0 = 3, which is not less than 3;

    - and 20*3 + 25*0 = 60 is not more than 100;



    - for the 2nd pair, I see that 4 + 0 = 4, which is not less than 3;

    - and 20*4 + 25*0 = 80 is not more than 100;



    - for the 3rd pair, I see that 1 + 3 = 4, which is not less than 3;

    - and 20*1 + 25*3 = 95 is not more than 100.
</pre>


Usually, "trial and error", or "guessing" are not considered as a strict mathematical method.


But if you CHECKED the results, similar to as I checked them, then it becomes ABSOLUTELY STRICT mathematical solution.



Have a nice day and happy learning (!)