Question 13336
You should first name the consecutive integers with variables.  Since you don't want more than one variable, you should link them all together.  I am going to call the first integer N.  The second one, since it is consecutive, is N+1.  The third one is N+2 (if you have a hard time thinking of this, think of the numbers 1, 2, and 3.  If 1 is N, you add one to it to get 2...then you add two to 1 to get 3).

Added together, the sum is 969...so your equation is {{{N + N + 1 + N + 2 = 969}}}.  To solve, combine like terms to get {{{3N + 3 = 969}}}.  Then solve the equation to get

{{{3N = 966}}}
{{{N = 322}}}

The three consecutive integers are 322, 323, and 324.