Solve for n; the largest integer would be n + 2.
Let a, b, c be three consecutive integers with a < b < c. So we have:
The sum of 3 consecutive integers: a + b + c
(Is) 75 less than 5 times the smallest integer: 5a - 75
So we have: a + b + c = 5a - 75.
If a, b and c are consecutives, and as we choose "a" as the smallest integer, then b = a+1 and c = a+2.
Thus: a + b + c = 5a - 75 => a + (a+1) + (a+2) = 5a - 75
3a + 3 = 5a - 75
-2a = -78
a = 39
The largest integer is c, wich is a + 2, so c = 41.