# If the sum of 3 consecutive even integers is 30 how do you find the numbers?

Sep 6, 2015

The three numbers are 9, 10, and 11

#### Explanation:

Let $n$ be the smallest of the three consecutive numbers
$\rightarrow$ the other two numbers are $n + 1$ and $n + 2$

We are told
$\textcolor{w h i t e}{\text{XXX}} \left(n\right) + \left(n + 1\right) + \left(n + 2\right) = 30$

$\rightarrow \textcolor{w h i t e}{\text{XX}} 3 n + 3 = 30$

$\rightarrow \textcolor{w h i t e}{\text{XX}} 3 n = 27$

$\rightarrow \textcolor{w h i t e}{\text{XX}} n = 9$

Sep 6, 2015

$8$, $10$ and $12$

#### Explanation:

We can define an even number as $2 x$

Let $2 x$ be the first even number

Let $2 x + 2$ be the next even number

Let $2 x + 4$ be the last one

Their sum is $30$ so we write

$2 x + \left(2 x + 2\right) + \left(2 x + 4\right) = 30$

Combining like terms

$6 x + 6 = 30$

$6 x = 24$

$x = 4$

So

$2 x = 2 \left(4\right) = 8$

$2 x + 2 = 8 + 2 = 10$

$2 x + 4 = 8 + 4 = 12$