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

Last updated date: 28th Mar 2023

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Answer

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Hint: In this question we have to find three consecutive odd numbers whose sum is 21. In order to find them, we will assume them as 2x - 1, 2x + 1 and 2x + 3. This will help us simplify the problem and solve the question.

Complete step-by-step answer:

We have to find three consecutive odd numbers whose sum is 21.

So, let the numbers be 2x - 1, 2x + 1 and 2x + 3.

So, (2x - 1) + (2x + 1) + (2x + 3) = 21

$ \Rightarrow $ 6x + 3 = 21

$ \Rightarrow $ 6x = 18

$ \Rightarrow $ x = 3

So, the numbers are 2(3) - 1,2(3) + 1 and 2(3) + 3.

That is; 5, 7, 9.

Note: Whenever we face such types of problems the crux point to remember is that we need to have a good grasp over linear equations. In these types of questions, we should always firstly assume the numbers and then apply the given constraints. This helps in getting us the required condition and gets us on the right track to reach the answer.

Complete step-by-step answer:

We have to find three consecutive odd numbers whose sum is 21.

So, let the numbers be 2x - 1, 2x + 1 and 2x + 3.

So, (2x - 1) + (2x + 1) + (2x + 3) = 21

$ \Rightarrow $ 6x + 3 = 21

$ \Rightarrow $ 6x = 18

$ \Rightarrow $ x = 3

So, the numbers are 2(3) - 1,2(3) + 1 and 2(3) + 3.

That is; 5, 7, 9.

Note: Whenever we face such types of problems the crux point to remember is that we need to have a good grasp over linear equations. In these types of questions, we should always firstly assume the numbers and then apply the given constraints. This helps in getting us the required condition and gets us on the right track to reach the answer.

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