# How do you find two consecutive odd integers whose sum is 116?

Apr 28, 2018

$57$ and $59$

#### Explanation:

Any odd integer can be written in the form of $2 n + 1$, where $n \in \mathbb{N}$, and even when $n = 0$.

So, the two consecutive odd integers would be $2 n + 1$ and $2 n + 1 + 2 = 2 n + 3$.

Therefore, we get:

$2 n + 1 + 2 n + 3 = 116$

$4 n + 4 = 116$

$4 n = 112$

$n = \frac{112}{4}$

$= 28$

$\therefore 2 n + 1 = 2 \cdot 28 + 1$

$= 57$

$2 n + 3 = 2 \cdot 28 + 3$

$= 59$

Therefore, the two consecutive integers are $57$ and $59$.