I don't know how your teacher chooses to solve this problem (or your text) but I do it this way.
Divide 81 by 3. You get 27.
Use 27 as your middle integer and go one odd integer up and down for the other 2.
25, 27, 29
the largest would be 29.
This works because 3 of the middle number equals 81, so the middle number plus a number 2 greater and a number 2 less would still be the same as adding 3 of the same number.
Check by adding the 3 numbers.
25 + 27 + 29 = 81
Let the integers be as followed.
X
X + 2
X + 4
Now, we can set up an equation to solve.
X + X + 2 + X + 4 = 81
3x + 6 = 81
-6 -6
3x = 75
X = 25
X = 25
X + 2 = 27
X + 4 = 29
Therefore, 29 is the largest integer.
