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

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Answer 1 · 2018-03-03T13:24:56

$22, 23, 24$

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:

Find the mean
Are they consecutive integers, odd integers or even integers?
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)