SOLUTION: Jayson needs to buy fruits. A mango (m) costs $20 each while a guava (g) costs $25 each. He can spend no more than $100. The total number of fruits is not less than 3. How many man

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Jayson needs to buy fruits. A mango (m) costs $20 each while a guava (g) costs $25 each. He can spend no more than $100. The total number of fruits is not less than 3. How many man      Log On


   

Question 1181027: Jayson needs to buy fruits. A mango (m) costs $20 each while a guava (g) costs $25 each. He can spend no more than $100. The total number of fruits is not less than 3. How many mango and guava can he buy? List 3 possible solutions and show a step by step solution on how you solved the problem.
Answer by ikleyn(52824) About Me  (Show Source):
You can put this solution on YOUR website!
.

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.


===================== 


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 (!)