Question

Find three consecutive whole numbers whose sum is 45 but less than 54

Answer 1

Answer:

15,16,17 or 16,17,18

Step-by-step explanation:

Define x:

Let x be the smallest number

The other 2 numbers are (x + 1) and (x + 2)

Solve x:

The sum is more than 45 but less that 54

45 < x + (x + 1) + (x + 2) < 54

45 < x + x + 1 + x + 2 < 54

45 < 3x + 3 < 54

42 < 3x < 51

42 < 3x < 51

14 < x < 17

So the smallest number must be between 14 and 17

⇒ The possible numbers are 15 and 16

If x = 15

x + 1 = 15 + 1 = 16

x + 2 = 15 + 2 = 17

Total sum = 15 + 16 + 17 = 48

If x = 16

x + 1 = 16 + 1 = 17

x + 2 = 16 + 2 = 18

Total sum = 16 + 17 + 18 = 51

Answer: The two possible set of numbers are 15 16 and 17 or 16, 17 and 18

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Answer 2

let the three consecutive numbers be x , x+1 , x+2

ATQ

45 < x + x +1 + x + 2 < 54

45 < 3(x+1) < 54

15 < x+1 < 18

14 < x < 17

x can be both 15 and 16

the set numbers are

the set numbers are (15 , 16 , 17 ) or (16 , 17 , 18 )

15 + 16 + 17 = 48

15 + 16 + 17 = 4816 + 17 + 18 = 51