# Two consecutive odd integers have a sum of 128, what are the integers?

May 10, 2018

$63 \text{ and } 65$

#### Explanation:

My strategy for doing problems like this is to divide $128$ in half, and take the odd integer directly above and below the result. Doing this for $128$ yields this:

$\frac{128}{2} = 64$

$64 - 1 = 63$
$64 + 1 = 65$

$63 + 65 = 128$

As $63$ and $65$ are two consecutive odd integers that sum to $128$, this satisfies the problem.

May 10, 2018

they are $63$ and $65$.

#### Explanation:

since the two numbers are odd, and consecutive, they have a difference of $2$.
suppose the smaller integer of the two $= x$
$128 = x + \left(x + 2\right)$
$= 2 x + 2$

so as to find the smaller odd integer, you need to find the value of $x$:
$128 - 2 = 2 x + 2 - 2$
$= 126 = 2 x$

$\frac{126}{2} = \frac{2 x}{2} = 63$

$x = 63$

63 is the smaller number, so the bigger number is $63 + 2 = 65$