Question

Three consecutive even integers have a sum of 36. Find the integers

Answer 1

To solve this, we must translate the sentence to an equation.

First, lets find an equation that can define all even integers.
Let $n$ be any integer (even or odd), then the equation for any even integer is:

$2n$

Now, lets start with an arbitrary even integer $2n$, then the next even integer will be $2(n+1)$, and the next will be $2(n+2)$.

So, if we want the sum of three consecutive even integers to be 36 we write:

$2n+2(n+1)+2(n+2)=36$

We can very easily solve for $n$:

$2n+2(n+1)+2(n+2)=6n+6=36$
$6n=30$
$n= \frac{30}{6}=5$

So, $n=5$.

If we plug in 5 to the equations of our three consecutive even numbers we get that the numbers are 10, 12, and 14.