Question

How do you find the two consecutive integers whose sum is $211$?

Answer 1

Hint: In this problem we need to find the two consecutive integers whose sum is $211$. So, we will first assume the two integers which are added to get the sum $211$ as $x$, $y$. Given that the two integers are consecutive i.e., the variables $x$ and $y$ are consecutive. We know that the consecutive terms are formed by adding one to before/previous term. So, we can write the variable $y$ as $x+1$. Now we will calculate the sum of the variables $x$ and $y$, simplify the equation by substituting the value of $y$. Now we will equate the obtained sum to $211$ and simplify the equation to get the required solution.

Complete step by step answer:
Let the two variables are $x$ and $y$.
If the above two variables are consecutive, then the value of $y$ must be equal to $x+1$. Mathematically
$y=x+1$.
Now the sum of the variables $x$ and $y$ is given by
$s=x+y$
Substituting $y=x+1$ in the above equation, then we will get
$\Rightarrow s=x+x+1$
Simplifying the above equation, then we will have
$\Rightarrow s=2x+1$
In the problem, they have mentioned that the sum of two consecutive variables is $211$. So, equating the sum to $211$, then we will get
$\Rightarrow 2x+1=211$
Subtracting $1$ on both sides of the above equation, then we will have
$\begin{align}
  & \Rightarrow 2x+1-1=211-1 \\
 & \Rightarrow 2x=210 \\
\end{align}$
Dividing the above equation with $2$ on both sides of the above equation, then we will get
$\begin{align}
  & \Rightarrow \dfrac{2x}{2}=\dfrac{210}{2} \\
 & \Rightarrow x=105 \\
\end{align}$
Now the value of $y$ will be
$\begin{align}
  & y=x+1 \\
 & \Rightarrow y=105+1 \\
 & \Rightarrow y=106 \\
\end{align}$

Hence the two consecutive numbers whose sum is $211$ are $105$, $106$.

Note: In this problem they have only mentioned two consecutive numbers, so we have taken them as $x$ and $y$ where $y=x+1$. If they have mentioned like three consecutive numbers, then we will assume $x$, $y$, $z$ where $y=x+1$, $z=y+1=x+2$. We will use the above values and follow the above procedure to find the required solution.