Three consecutive integers have a sun of 51. find the i ntergers

There is a quick way to find the answer to these types of questions. First, divide 51 by 3, since our consecutive integers will be in that number range.
51 / 3 = 17.
Our consecutive numbers lie around 17.
Next, find 3 consecutive numbers in the ones place (5#.00, # being the ones place) that add up to 11, 21, 31, 41, or 51 (if possible).
6, 7, and 8 add up to a number that ends in the ones place.
Let's try 16, 17, and 18 as our consecutive numbers, since they lie around 17, and add up to a number with a 1 in the ones place.
16 + 17 = 33.
33 + 18 = 51.
Your consecutive numbers are:
16, 17, and 18.
I hope this helps!