✒️[tex]\large{\mathcal{ANSWER}}[/tex]
[tex]===============[/tex]
The highest number is 139 , so the correct alternative is the letter C.
● But how do you know this?
- Well , the question told us that the sum of 3 consecutive natural numbers is 414 , that said , it asks us , which is the largest of these 3 numbers.
Let's call these numbers x , however , since they are consecutive , we can build a first degree equation such that :
[tex]x + x + 1 + x + 2 = 414 \\ 3x + 3 = 414 \\ 3x = 414 - 3 \\ 3 = 411 \\ 3x = \frac{411}{3} \\ \: \boxed{x = 137} [/tex]
● Since we've found the starting number, let's just replace the values:
[tex]x = 137[/tex]
[tex]x + 1 = 137 + 1 =\: \boxed{138} [/tex]
[tex]x + 2 = 137 + 2 = \: \boxed{139} [/tex]
Therefore , we can conclude that the largest number is 139 , and this number is present in alternative C.
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Good studies and I hope I have helped.
