Answer:
The greatest of the three consecutive integers is 17.
Step-by-step explanation:
Let's assume the first integer as x. Then, the second and third consecutive integers can be represented as x+1 and x+2 respectively.
According to the problem statement, the sum of three consecutive integers is 51. So, we can write an equation as:
x + (x+1) + (x+2) = 51
By solving the above equation, we can find the value of x as:
x + x + 1 + x + 2 = 51
3x + 3 = 51
3x = 48
x = 16
Now that we have found the value of x, we can find the other two consecutive integers as:
x+1 = 16+1 = 17
x+2 = 16+2 = 18
Therefore, the greatest of the three consecutive integers is 17.
