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in Linear Equations by (34.5k points)
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Find three consecutive whole numbers whose sum is more than 45 but less than 54.

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Best answer

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.

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