Question

How do you find two consecutive integers whose sum is $45?$

Answer 1

Hint: First consider one of the number to be some variable, and let that variable is the greater one in the consecutive numbers then the second number will be written as variable minus one, then perform the operation between them according to the question, and simplify the equation using algebraic operations, send variables to the left hand side and constants to the right hand side and then divide both sides with coefficient of the variable you will get the value of one number, accordingly calculate the another one.

Complete step by step solution:
In order to find two numbers whose sum is equals to $45$, we need to consider the numbers to be variable first. So let us consider the smaller one to be $x$. Since both numbers are consecutive numbers. Therefore another number will be $x+1$. Now according to the question,
$x+(x+1)=45$
Solving this equation, we will get the required numbers,
$$\begin{gathered} \Rightarrow x+(x+1)=45 \\ \Rightarrow x+x+1=45 \\ \Rightarrow 2x+1=45 \end{gathered}$$
Subtracting $1$ from both the sides we will get,
$$\begin{gathered} \Rightarrow 2x+1-1=45-1 \\ \Rightarrow 2x=44 \end{gathered}$$
Now dividing both sides with coefficient of $x$ that is $2$, we will get
$$\begin{gathered} \Rightarrow {\displaystyle \frac{2x}{2}}={\displaystyle \frac{44}{2}} \\ \therefore x=22 \end{gathered}$$
So we get the value of the smaller number which is equal to $22$.
Larger one will be given as $x+1=22+1=23$.

Therefore the required set of two consecutive numbers whose sum is $45\text{is}22\text{and}23$.

Note: In order to solve this type of word problems where the values are need to be found, your first step should be to consider the required numbers as variables and then write the equation according to the question with help of the considered variables and solve further. One more thing, the result doesn’t matter if we have considered the greater number and write a smaller one accordingly.