Question

The sum of three consecutive odd numbers is 21. Find the numbers.​

Answer 1

Let the numbers be

2x+1 ,2x+3 and 2x+5 { as 2x is a even number so adding consecutive odd numbers will make it odd}

A.T.Q

2x+1 +2x+3 +2x+5 = 21

= 6x+9= 21

= 6x= 21 - 9

6x = 12

X = 12/ 6

X = 2 so numbers are

2×2+1 = 5 , 2×2+3 = 7 and 2×2+5=9

5,7,9
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Answer 2

ANSWER :

• If the sum of three consecutive odd numbers is 21, then the numbers are : 5, 7 and 9.

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SOLUTION :

Given :-

• Sum of three consecutive odd numbers = 21

To Find :-

• The three consecutive odd numbers = ?

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Method 1 :-

Let,

• The first odd number = 2x + 1

• The second consecutive odd number = 2x + 3

• The third consecutive odd number = 2x + 5

According to Question,

• (2x + 1) + (2x + 3) + (2x + 5) = 21

➨ 2x + 1 + 2x + 3 + 2x + 5 = 21

➨ 2x + 2x + 2x + 1 + 3 + 5 = 21

➨ 6x + 9 = 21

➨ 6x = 21 - 9

➨ 6x = 12

➨ x = $\dfrac{12}{6}$

∴ x = 2

Putting the value of x, we get,

• The first odd number = 2x + 1 = (2 × 2) + 1 = 4 + 1 = 5

• The second consecutive odd number = 2x + 3 = (2 × 2) + 3 = 4 + 3 = 7

• The third consecutive odd number = 2x + 5 = (2 × 2) + 5 = 4 + 5 = 9

Therefore, the three consecutive odd numbers are : 5, 7 and 9.

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Method 2 :-

Let,

• The first odd number = x

• The second consecutive odd number = x + 2

• The third consecutive odd number = x + 4

According to Question,

• x + (x + 2) + (x + 4) = 21

➨ x + x + 2 + x + 4 = 21

➨ x + x + x + 2 + 4 = 21

➨ 3x + 6 = 21

➨ 3x = 21 - 6

➨ 3x = 15

➨ x = $\dfrac{15}{3}$

∴ x = 5

Hence,

• The first odd number = x = 5

• The second consecutive odd number = x + 2 = 5 + 2 = 7

• The third consecutive odd number = x + 4 = 5 + 4 = 9

Therefore, the three consecutive odd numbers are : 5, 7 and 9.