Question

Express $169$ as sum of two consecutive numbers.

Answer 1

Hint: To solve this question we need to know about the consecutive numbers. Consecutive numbers are the numbers which follow each other continuously in the order from smallest to largest. To solve this question we will consider two unknown variables which are $x$ and $x+1$.

Complete step by step answer:
The question asks us to find the numbers which sum up to give $169$ as the result. The first step is to consider a variable $x$ which is one of the terms and another term which gets added in $x+1$. On writing the above explanation mathematically we get:
$\Rightarrow {{1}^{st}}term+{{2}^{nd}}term=169$
So the first and the second terms are the unknown variable given above which are:
$\Rightarrow x+\left( x+1 \right)=169$
On calculating the terms we get:
$\Rightarrow 2x+1=169$
Taking the term $1$ to Right Hand Side to find the value of $x$, we get:
$\Rightarrow 2x=169-1$
$\Rightarrow 2x=168$
On dividing both the terms in Left Hand Side and in Right Hand Side by $2$ to get the value of $x$ is:
$\Rightarrow \dfrac{2x}{2}=\dfrac{168}{2}$
$\Rightarrow x=84$
Since the value of $x$ is $84$, so the value of $x+1$ will be $84+1$ which is $85$.
$\therefore $ The two consecutive numbers which sum to $169$ are $84$ and $85$.

Note: We can check whether the answer we got, which are $84$ and $85$ is correct or not. So for this we will add two numbers and see that the sum of the numbers results in the number given in the question which is $169$in the case given. On writing it mathematically we get:
$\Rightarrow 84+85$
$\Rightarrow 169$
Since by adding the two numbers we get $169$ as the result, hence the answers we got are correct. Also we can see that the two numbers are consecutive which is asked in the question.