Question

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

Answer 1

`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=3x`

The sum of these numbers equal `69`: `3x=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)