Question

Three consecutive integers have a sum of `258` What are the integers?

Answer 1

`85,86,87`

Explanation:

Consecutive integers are numbers that follow each other without any gaps like:

`3,4,5` or `16,17,18`

We're going to call the first number in the series `N`, the next one `N+1` because it is 1 greater than N, and the last one `N+2` because it is 2 greater than N.

We know that the sum of all three numbers is `258`, so we can make this equation:

`N + (N+1)+(N+2) = 258`

Add like terms together, then simplify:
`color(blue)N + color(blue)N+1+color(blue)N+2 = 258`
`color(blue)"3N" + 3 = 258`
`3N = 255`
`N = 85`

The first number is 85, so the three consecutive integers are:
`85,86,87`

Answer 2

The integers are `85 , 86` and `87`

Explanation:

Let the first integer of the three be `n` then the integers following `n` is `n+1` and `n+2`

The sum means to add...

`n + (n+1) + (n+2) = 258`

Collecting like terms...

`3n+ 3 = 258`

Subtracting 3 from both sides...

`3n = 255`

Dividing by 3 on both sides to just get `n`

`=> n = 255/3 = 85`

Hence `n+1 = 86` and `n+2 = 87`

Hence the integers are `85 , 86` and `87`