# The sum of three consecutive even integers is 30 more than the largest. What are the integers?

Nov 27, 2016

See explanation.

#### Explanation:

First we have to write the given data in mathematical terms.

The three consecutive even numbers can be written as $2 n$, $2 n + 2$ and $2 n + 4$.

From the first sentence of the task we can deduce that the sum of $2 n$ and $2 n + 2$ is $30$.

$2 n + 2 n + 2 = 30$

$4 n + 2 = 30$

$4 n = 28$

$n = 7$

Now we can calculate the numbers and write the answer:

$2 n = 14$; $2 n + 2 = 16$ and $2 n + 4 = 18$

Answer: The numbers are: 14, 16 and 18

Nov 27, 2016

14, 16, 18

#### Explanation:

Let $n$ be the smallest positive integer in the sequence

Hence the sum on the three even integers is: $n + \left(n + 2\right) + \left(n + 4\right)$

We are told that this sum is 30 more than the largest which must be $\left(n + 4\right)$

$\therefore n + \left(n + 2\right) + \left(n + 4\right) = 30 + \left(n + 4\right)$

$3 n + 6 = n + 34$

$2 n = 28$

$n = 14$

Hence the sequence is: 14, 16, 18

To check:
$14 + 16 + 18 = 48$
$48 = 18 + 30$