# The sum of two consecutive odd integers is 124, what are the integers?

Feb 7, 2016

$61$ and $63$

#### Explanation:

An odd integer can be written as:
$\left(2 n + 1\right)$
If the odd integers are consecutive, then the next odd integer will be:
$\left(2 \left(n + 1\right) + 1\right) = \left(2 n + 3\right)$

Given that the sum of these integers comes to $124$ we can write an equation and then solve for $n$:

$\left(2 n + 1\right) + \left(2 n + 3\right) = 124$
$4 n + 4 = 124$
$4 n = 120$
$\to n = 30$.

That would mean that our odd integers are:

$2 \left(30\right) + 1$ =61
and #2(30)+3 = 63

And of course $61 + 63 = 124$.