# How do you find four consecutive even integers whose sum is 42?

Oct 30, 2016

There are no possible even integers which add to 42.

#### Explanation:

Consecutive numbers are separated by 1.
Consecutive odd or even numbers are separated by 2.

Define the consecutive even numbers with variable first.

Let the first even number be $x$.
The next three are #(x+2), (x+4), (x+6)

Their sum is 42. Write an equation...

$x + x + 2 + x + 4 + x + 6 = 42$

$4 x + 12 = 42$

$4 x = 42 - 12$

$4 x = 30$

$x = 7 \frac{1}{2}$

This is not an even integer.
There are no consecutive even integers which add up to 42.

Check:
$8 + 10 + 12 + 14 = 44$
$6 + 8 + 10 + 12 = 36$