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= (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.