Question

The sum of three consecutive even integers is \[180\]. How do you find the numbers?

Answer 1

Hint: From the question, we had been given that the sum of three consecutive even integers is \[180\]. And, we have been asked to find the numbers. We can find the numbers by assuming the numbers as some variables and it has been clearly mentioned that the three numbers are consecutive. So, if we assume one number, we can get the others.

Complete step by step answer:
Now consider the question it is given that the sum of three consecutive even integers is $ 180 $.
First, let us assume the middle term as \[2n\]
As it has been given that the integers are even, we assumed the number as multiple of \[2\]
 Since, our middle term is \[2n\], the other two terms will be \[2n-2,2n+2\].
As it had been given in the question that the three numbers are consecutive.
Therefore, the three numbers are \[2n-2,2n,2n+2\]
Also, in the question, we had been given that,
The Sum of the three consecutive integers is \[180\]
By the above statement, we can write \[2n-2+2n+2n+2=180\]
By simplifying the above equation, we get
\[6n=180\]
\[\Rightarrow n=\dfrac{180}{6}\]
\[\Rightarrow n=30\]
But we are not done yet. We have just got the value of \[n\].
We should substitute the value of \[n\] in the assumed numbers to get the original numbers.
By substituting the value of \[n\] in the assumed numbers, we get
The first number \[2n=2\left( 30 \right)=60\]
The second number \[2n-2=2\left( 30 \right)-2=60-2=58\]
The third number \[2n+2=2\left( 30 \right)+2=60+2=62\]
Therefore, the numbers are \[58,60,62\].

Note:
 We should assume the numbers correctly in this type of question. We should be well aware of the assumption of numbers. Also, we should be very careful while doing the calculation part. We should understand the question very keenly so that we can solve the given question very easily. This can be also done by assuming the numbers as $ x $, $ x+2 $