Answer :
Let's solve the problem using algebra. We are looking for three consecutive odd numbers. Let's denote the smallest odd number as n. Since the numbers are consecutive odd numbers, the next two will be n + 2 and n + 4 respectively.
According to the problem, the sum of these three numbers is 255:
n + (n + 2) + (n + 4) = 255
We can combine like terms:
3n + 6 = 255
Now, we'll subtract 6 from both sides of the equation to isolate 3n:
3n = 249
Next, we'll divide both sides by 3 to find n:
n = 249 / 3
n = 83
This is the smallest number. Since we're looking for the largest number in the sequence of consecutive odd numbers, we'll add 4 to it (because the problem tells us that the numbers are consecutive odd numbers, so one will be two more than the smallest, the next will be two more than the second, therefore four more than the smallest):
largest number = n + 4
largest number = 83 + 4
largest number = 87
So, the value of the largest number is 87, which corresponds to option E.
