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Question
Find three conescutive whole numbers whose sum is more than 45 but less than 54.
Solution
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, and (17 + 1)
i.e., 16, 17, 18.
∴ The three consecutive whole numbers are 15, 16, 17 or 16, 17, 18.
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