# The sum of three consecutive odd integers is 63, what are the three integers?

Feb 1, 2016

first integer$= 19$
second integer$= 21$
third integer $= 23$

#### Explanation:

To solve this problem, we will need to set up an equation. But first, we need to make let statements to let others know what each variable or expression represents. Since each consecutive odd integer is separated by a difference of $2$, your let statements are:

Let $x$ be the first integer.
Let $x + 2$ be the second integer.
Let $x + 4$ be the third integer.

The sum of the three consecutive odd integers is $63$, so your equation is:

$\left(x\right) + \left(x + 2\right) + \left(x + 4\right) = 63$

Then solve for $x$:

$\left(x\right) + \left(x + 2\right) + \left(x + 4\right) = 63$

$x + x + 2 + x + 4 = 63$

$3 x + 6 = 63$

$3 x + 6$ $\textcolor{red}{- 6} = 63$ $\textcolor{red}{- 6}$

$3 x = 57$

$3 x \textcolor{red}{\div 3} = 57 \textcolor{red}{\div 3}$

$x = 19$

Now that you know your first integer has a value of $19$, substitute $x = 19$ into $x + 2$ and $x + 4$ to find the values of the second and third integers.

$x + 2 \textcolor{w h i t e}{X X X X X X X X X X X X} x + 4$

$= \left(19\right) + 2 \textcolor{w h i t e}{X X X X X X X X X} = \left(19\right) + 4$

$= 21 \textcolor{w h i t e}{X X X X X X X X X X X X} = 23$

$\therefore$, the integers are $19$, $21$, and $23$.