You can write two consecutive integers as x and x+1.
So, if you want their sum to be smaller than 209, you must write
[tex] x+(x+1) \leq 209 \iff 2x+1 \leq 209[/tex]
Subtract 1 from both sides:
[tex] 2x \leq 208[/tex]
Divide both sides by 2:
[tex] x \leq 104[/tex]
So, the two integers are 104 and 105, and their sum is indeed 209.
Note that 105 is the largest possible number. You may also pick smaller numbers, like 10 and 11, because their sum is 21, which is no more than 209.
