# The sum of 3 consecutive odd integers is 105, how do you find the numbers?

Apr 15, 2016

$33 , 35 , \mathmr{and} 37$

#### Explanation:

Let the middle number of the three consecutive odd numbers be $n$.
Therefore the other two numbers will be $n - 2$ and $n + 2$

$\textcolor{w h i t e}{\text{XXX}} n - 2$
$\textcolor{w h i t e}{\text{XXX}} n$
color(white)("X")underline(+color(white)("X") n+2)
$\textcolor{w h i t e}{\text{XXX")3ncolor(white)("XXXX}} = 105$

$\rightarrow n = 35$
and the other two numbers are $33$ and $37$

Apr 15, 2016

33,35,37

#### Explanation:

First of all lets say the unknown numbers are $x - 2 , x \mathmr{and} x + 2$.
We can represent it like this because the question says that they are consecutive odd numbers, and by definition they will differ by 2 each time

By summing these terms together, we can solve for $x$:
$105 = x - 2 + x + x + 2$
$105 = 3 x$
$x = 35$
Now that we have $x$, we can say the the consecutive odd numbers are $35 - 2 , 35$ and $35 + 2$, which are 33,35,37