SOLUTION: The sum of three consecutive odd integers is 16 more than the greatest of the integers. Find the integers.

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Question 216936: The sum of three consecutive odd integers is 16 more than the greatest of the integers. Find the integers.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Let the first odd integer be (2n+1) where n is any integer, the (2n+3) is the next consecutive odd integer and (2n+5) is the third consecutive odd integer.
The sum of these is 16 more than the third (largest) of the integers.
%282n%2B1%29%2B%282n%2B3%29%2B%282n%2B5%29+=+%282n%2B5%29%2B16 Simplify.
6n%2B9+=+2n%2B21 Subtract 2n from both sides.
4n%2B9+=+21 Subtract 9 from both sides.
4n+=+12 Divide both sides by 4.
n+=+3 so...
2n%2B1+=+7
2n%2B3+=+9
2n%2B5+=+11