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

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

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



Now, lets start with an arbitrary even integer , then the next even integer will be , and the next will be .

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



We can very easily solve for :





So, .

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