# The sum of three consecutive even #s is 144; what are the numbers?

May 30, 2016

They are 46, 48, 50.

#### Explanation:

An even number is a multiple of $2$, then can be written as 2n. The next even number after $2 n$ is $2 n + 2$ and the following is $2 n + 4.$
So you are asking for which value of $n$ it you have

$\left(2 n\right) + \left(2 n + 2\right) + \left(2 n + 4\right) = 144$

I solve it for $n$

$6 n + 6 = 144$
$n = \frac{138}{6} = 23$.

The three numbers are

$2 n = 2 \cdot 23 = 46$
$2 n + 2 = 46 + 2 = 48$
$2 n + 4 = 46 + 4 = 50$

May 30, 2016

The numbers are 46, 48 and 50.

#### Explanation:

First define the consecutive even numbers:

Even numbers, such as 8, 10, 12 etc. differ by 2.

We could call the numbers $x , x + 2 \mathmr{and} x + 4$, but there is no guarantee that x is even.

However, an even number can be divided by 2, so any number given as $2 x$ is definitely even.

SO, let the consecutive even numbers be $2 x , 2 x + 2 \mathmr{and} 2 x + 4$
Their sum is 144, so write an equation:

$2 x + \left(2 x + 2\right) + \left(2 x + 4\right) = 144$

$6 x + 6 = 144$
$6 x = 138$
$x = 23$

However, we defined the first even number as $2 x$.

$2 \times 23 = 46$

The numbers are 46, 48 and 50.