Question

Cooper, Sha'NiyaThe sum of three consecutive integers is 177. What is the largest of the integers, and why?

Answer 1

We can represent the sum of the three consecutive integers as:

$n+(n+1)+(n+2)=177$

Then, we need to solve the equation for n, then:

$3n+3=177_{}\Rightarrow3n=177-3\Rightarrow3n=174\Rightarrow n=\frac{174}{3}\Rightarrow n=58$

Then, the largest of the integers is n + 2 or 58 +2 = 60.

The reason is that the other integers are 58, 58 + 1 = 59, that is, 58 and 59.

We can check that:

58 + 59 + 60 = 177.