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)