FIND THREE CONSECUTIVE ODD INTERGERS WITH THE SUM OF 63

Any odd integer can be expressesd as 2n-1 where n = 1, 2, 3......

So, let the first odd integer be 2n-1, the next one 2n+2, and the last one 2n+3.

So

(2n-1) + (2n+1) + (2n+3) = 63     and simplifying, we have

6n + 3 = 63  

6n = 60

n=10

So

The first integer is 2(10) - 1 = 19

The next one is 2(10) + 1 = 21

And the last one is 2(10) + 3 = 23

And that's it!!

let the integers be a, a+2 and a+4 can you take it from there?

Yes CPill's choice is better.  The algebra is easier.  

Eh....not necessarily better....just different........we would have both arrived at the same train station......so to speak......