Question

Three consecutive intergers have a sum of 54. Find the integers

Answer 1

Let's take a look at three very familiar consecutive integers before we get more abstract with it: 1, 2, and 3. How do 2 and 3 relate to 1? Well, 2, is 1 + 1, and 3 is 1 + 2. If we look at that integers 5, 6, and 7, we see a similar pattern; 6 is 5 + 1, and 7 is 5 + 2. In general, if we want to look at any 3 consecutive integers starting with some integer
`n`, the following integers will be
`n+1` and
`n+2`.

We want to find 3 consecutive integers that add up to 54, so we'll need to add
`n`,
`n+1`, and
`n+2` together, set their sum equal to 54, and solve for
`n` to find them.


`n+(n+1)+(n+2)=54`

Combining like terms on the left side:


`(n+n+n)+(1+2)=54\\ 3n+3=54`

And solving for
`n`:


`3n+3=54\\ 3n=51\\ n=17`

The first of the three consecutive integers is 17, which means the next two must be 18 and 19. Checking our work, we find that indeed:


`17+18+19=54\\ 35+19=54\\ 54=54`

Our three integers are 17, 18, and 19.

Answer 2

This is asking what two numbers add up to 54.
That will be 17 and 18 and 19.
They add up to 54.

Hope this is what you're looking for.
Hope this helps :)