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in Linear Equations by (49.3k points)
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(i) The sum of three consecutive natural numbers is 36. What are the numbers 

(ii) The sum of three consecutive even numbers is 36. What are the numbers? 

(iii) Can the sum of three consecutive odd numbers be 36. Why? 

(iv) The sum of three consecutive odd numbers is What are the numbers? 

(v) The sum of three consecutive natural numbers is 33. What are the numbers?

1 Answer

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by (51.8k points)
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Best answer

 (i) x + x + 1 + x + 2 = 36

3x + 3 = 36

x = \(\frac{36-3}{3}\) = 11

∴ Numbers are 11, 12, 13

x – 1 + x + x + 1 = 36

3x = 36

x = 12

Or

∴ Numbers are 11, 12, 13

(ii) (x – 2) + x + (x + 2) = 36

3x = 36

x = 12

∴ The numbers are 10, 12, 14

(iii) The sum of three odd numbers is odd. 

∴ It is not possible to get 36 as the sum of three odd numbers. 

(iv) (x – 2) + x + (x + 2) = 33 

3x = 33 

x = 11 

∴ Numbers are 9, 11, 13 

(v) (x – 1)+ x + (x + 1) = 33 

3x = 33 

x = 11 

The numbers are 10, 11, 12

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