The sum of three consecutive odd integers is 177, what are the integers?

Jun 28, 2015

$\left\{57. 59 , 61\right\}$

Explanation:

Let the three consecutive odd integers be
$\textcolor{w h i t e}{\text{XXXX}}$$2 x - 1 , 2 x + 1 , \mathmr{and} 2 x + 3$

We are told
$\textcolor{w h i t e}{\text{XXXX}}$$\left(2 x - 1\right) + \left(2 x + 1\right) + \left(2 x + 3\right) = 177$
which implies
$\textcolor{w h i t e}{\text{XXXX}}$$6 x + 3 = 177$

$\textcolor{w h i t e}{\text{XXXX}}$$\rightarrow 6 x = 174$

$\textcolor{w h i t e}{\text{XXXX}}$$\rightarrow x = 29$

So the numbers are
$\textcolor{w h i t e}{\text{XXXX}}$$\left\{2 \left(29\right) - 1 , 2 \left(29\right) + 1 , 2 \left(29\right) + 3\right\}$

$\textcolor{w h i t e}{\text{XXXX}}$$= \left\{57 , 59 , 61\right\}$