# Two consecutive odd integers have a sum of 48, what are the two odd integers?

Jan 27, 2016

23 and 25 together add to 48.

#### Explanation:

You can think of two consecutive odd integers as being value $x$ and $x + 2$. $x$ is the smaller of the two, and $x + 2$ is 2 more than it (1 more than it would be even). We can now use that in an algebra equation:

$\left(x\right) + \left(x + 2\right) = 48$

Consolidate left side:
$2 x + 2 = 48$

Subtract 2 from both sides:
$2 x = 46$

Divide both sides by 2:
$x = 23$

Now, knowing that the smaller number was $x$ and $x = 23$, we can plug $23$ into $x + 2$ and get $25$.

Another way to solve this requires a bit of intuition. If we divide $48$ by $2$ we get $24$, which is even. But if we subtract $1$ from it, and add $1$ as well, we can get the two odd numbers that are next to it.