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I just solved this problem under this link
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
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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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
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,
- 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.
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 (!)