# If the sum of three consecutive integers is 69, what are the integers?

Mar 3, 2018

$22 , 23 , 24$

#### Explanation:

Algebra method:

Let $x$ be the middle number.

Then the three numbers are: $x - 1 , x , x + 1$

The sum of these numbers: $x - 1 + x + x + 1 = 3 x$

The sum of these numbers equal $69$: $3 x = 69$

Solve for $x$

$x = 23$

Substitute $x = 23$ into $x - 1$ and $x + 1$: $23 - 1 = 22 , 23 + 1 = 24$

Check: $22 + 23 + 24 = 69$ and they are consecutive.

Normally though, my thinking process would be like this:

1. Find the mean
2. Are they consecutive integers, odd integers or even integers?
3. If they're consecutive, +1 and -1 to the mean. If they're odd/even, +2 and -2 to the mean. (Of course it would be different if there are 5 consecutive numbers, 7, etc)