Let the three consecutive whole numbers be (x – 1),
x and (x + 1).
∴ Sum of the three numbers
= (x – 1) + x + (x + 1)
= 3x
Given that, the sum of the three numbers is greater than 45 and less than 54.
When the sum of the three numbers is 45,
3x = 45
∴ x = 45/3
∴ x = 15
When the sum of the three numbers is 54,
∴ 3x = 54
∴ x = 54/3
∴ x = 18
∴ the value of x is greater than 15 and less than 18.
∴ the value of x is either 16 or 17.
Case I:
If the value of x is 16, then the three consecutive whole numbers are (16 – 1), 16,(16 + 1)i.e., 15, 16, 17
Case II:
If the value of x is 17, then the three consecutive whole numbers are (17 – 1), 17, (17 + 1)
i.e., 16, 17, 18.
∴ The three consecutive whole numbers are 15, 16, 17 or 16, 17, 18.