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Find two consecutive positive integers, where the sum of numbers is equal to 365.

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Last updated date: 24th Jun 2024
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Answer
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Hint: The two consecutive numbers are in the form of $x$ and $x + 1$. The given sum of these two numbers is $365$ . This implies that $(x) + (x + 1) = 365$. Solve these linear equations to get the desired answer.

Complete step-by-step answer:
Given, the sum of two consecutive positive integers is 365.
Let the first positive be $x$ and the second positive integer will be $x + 1$
Given, the sum of two consecutive positive integers is 365.
$ \Rightarrow (x) + (x + 1) = 365$
on adding this,
$ \Rightarrow 2x + 1 = 365$
On solving this equation, we will get
$ \Rightarrow 2x = 364$
$ \Rightarrow x = 182$
The number is x i.e., 182 and x+1 i.e., 183

Therefore, two consecutive numbers are 182 and 183.

Note: This question can also be solved by trial and error method. You could solve this question a few different ways, and one of those is by the guess and check method. Start by taking two numbers, say 180 and 181, and add them together. You would find the answer to be 361. You then realize that you need 4 more to make 365.
You can choose higher numbers, such as 182 and 183 until you find the pair that works. This is called the trial and error method.
One more example of such a question is to find the numbers whose two consecutive integers have the sum of 35.
By the guess and check method. Start by taking two numbers, say 15 and 16, and add them together. You would find the answer to be 31. You then realize that you need 4 more to make 35.
You can choose higher numbers, such as 16 and 17 until you find the pair that works.
$ \Rightarrow 16 + 17 = 35$
The numbers are 16 and 17.