Question

The sum of three consecutive odd numbers is 45.Find the largest of the three numbers.​

Answer 1

The average would be 15; the numbers would be 13, 15, 17. Can be done, also, by Algebra: x-2, x & x+2 are the numbers; set their sum to 45 and solve.

Answer 2

Given:-

• The sum of three consecutive odd numbers is 45.

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To Find:-

• Find the largest of the three numbers.

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Concept:-

• Let's understand the concept first.Form an equation according to the conditions mentioned in the question by taking unknown consecutive numbers and solve it.Then,Find the value of the unknown number and substitute it.

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Solution:-

Let the three consecutive odd numbers be x,x + 1,x + 2

Given that!

The sum of three consecutive odd numbers is 45.

According to the question we have!

⟹ x + x + 1 + x + 2 = 45

⟹ (x + x + x) + (1 + 2) = 45

⟹ 3x + 3 = 45

⟹ 3x = 45 - 3

⟹ 3x = 42

⟹ x = 42/3

⟹ x = 14

The first odd number is 14.

Substitute the value of x in consecutive odd numbers we had taken!

For x + 1,

⟹ x + 1

⟹ 14 + 1

⟹ 15

Hence,

The second consecutive odd number is 15.

For x + 2,

⟹ x + 2

⟹ 14 + 2

⟹ 16

Hence,

The third consecutive odd number is 16.

Therefore,

The three consecutive odd numbers are 14,15 and 16 .The largest of these numbers is 16.

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Verification:-

x + x + 1 + x + 2 = 45

x = 5

⟹ 14 + 14 + 1 + 14 + 2 = 45

⟹ 43 + 2 = 45

⟹ 45 = 45

⟹ LHS = RHS

Hence,

It is verified.

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