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The sum of two consecutive even numbers is 38. How do you find the numbers?

seo-qna
Last updated date: 20th Jun 2024
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Answer
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Hint:In the given question, we have asked to find the numbers and it is given that the sum of those two even consecutive numbers is 38. In order to solve the given question, first we assume two consecutive even numbers and according to the question, we equate the addition of two consecutive even numbers equal to 38 and simplify.

Complete step by step solution:
We have given that,
The sum of two consecutive even numbers is 38.
Now,
Let’s assume the two consecutive even numbers are \[x\] and\[x+2\].
According to the question,
Sum of \[x\] and \[x+2\] is equal to 38.
We have,
\[\Rightarrow x+\left( x+2 \right)=38\]
Simplifying the above, we get
\[\Rightarrow x+x+2=38\]
Combining the like terms, we get
\[\Rightarrow 2x+2=38\]
Subtracting 2 from both the sides of the equation, we get
\[\Rightarrow 2x+2-2=38-2\]
\[\Rightarrow 2x=36\]
Dividing both the sides of the equation by 2, we get
\[\Rightarrow x=18\]
Thus,
First even number is 18.
Now, the second even number will be = \[x+2=18+2=20\]
Therefore, the consecutive even numbers are 18 and 20.

Note:
Students should always remember that the even numbers are those numbers that are divisible by 2.
Here consecutive even numbers means the numbers which come one after one and that are divisible by 2 i.e. even numbers. The main point is this question is that we assume a second consecutive even number is x+2 instead of x+1 as if we add 1 to any even number, it will become an odd number. For example; first even number is 14 and if we add 1 to it, it will become 15 which is an odd number not the even number.