Question

The sum of two consecutive integers is $47$, how do you find the two numbers?

Answer 1

Hint: We take the unknown number as $x$ and $x + 1$ as they are two consecutive numbers. We add them up and equate with $47$ , according to given. We solve the equation further and get our required numbers.

Complete step-by-step solution:
In the given question we have, that two integers add up to give the number $47$.
Now let the two numbers is: $x$ and \[\left( {x + 1} \right)\] since they are two consecutive digits, means they are just one after the other thus we add $ + 1$ to the second number.
According to the sum: $x + \left( {x + 1} \right) = 47$, if we solve this equation then we can get our required numbers.
$ \Rightarrow x + x + 1 = 47$
On simplifying it further, we get:
$ \Rightarrow 2x + 1 = 47$
On adding $ - 1$ to both sides, we get:
$ \Rightarrow 2x = 47 - 1 = 46$
Now dividing both sides with $2$, we get:
$x = \dfrac{{46}}{2} = 23$
Thus the number is $23$ and $23 + 1 = 24$

23 and 24 are the required integers.

Note: These types of questions are called story sums. In order to solve these sums accurately, one must thoroughly read and understand what the question requires. We form our equation accordingly once we have found what we need to place as our unknown constant and relate it with the other variables in the question.
An alternate way of doing this sum is that instead of taking our numbers as $x$ and $\left( {x + 1} \right)$ , we can take the first number as $\left( {x - 1} \right)$ and second number as $x$.
Let’s form an equation using these two numbers.
According to the given:
$\left( {x - 1} \right) + x = 47$
On simplifying it, we get:
\[ \Rightarrow x - 1 + x = 47\]
$ \Rightarrow 2x - 1 = 47$
On adding $ + 1$ to both the sides, we get:
$ \Rightarrow 2x = 47 + 1 = 48$
Let us divide the term and we get,
$ \Rightarrow x = \dfrac{{48}}{2} = 24$
$ \Rightarrow x = 24$
Thus the two numbers are: $\left( {x - 1} \right)$ and $x$ $ = 23$ and $24$