Question

A number is such that it is as much greater than $45$ as it is less than $75$. Find the number.

Answer 1

Hint: First of all, assume a variable as the required number. Now find the differences between the given limits and the required variable, and equate them to get the result. For example, if we subtract $20$ from $50$ we get $30$ from this we can say that $20$ is $30$ less than $50$. Also, if we add $50$ to $70$ then we get $120$ i.e. $120$ is $50$ greater than $70$.

Complete step by step answer:
$\Rightarrow$ Let us take a number $x$ which is greater than $45$ as it is less than $75$.
 If $x$ is greater than $45$ then the difference between the two numbers is
$\Rightarrow$ $y=x-45$
Where $y$ is the difference between $x$ and $45$.
If $x$ is less than $75$ then the difference between the two numbers is
$\Rightarrow$ $z=75-x$
Where $z$ is the difference between the $x$ and $75$.
$\Rightarrow$ To find the number which is greater than $45$ and less than $75$, we are going to equate the difference that are calculated above. Then
$\begin{align}
  & y=z \\
 & x-45=75-x \\
 & x+x=75+45 \\
 & 2x=120 \\
 & x=\dfrac{120}{2} \\
 & x=60
\end{align}$
$\Rightarrow$ So the number which is less than $45$ and greater than $75$ is $60$.

Note:
 You can solve the problem in another method that finds the difference between the given limits i.e. $75-45=30$ and do half the obtained difference i.e. $\dfrac{30}{2}=15$. Now add that value to the lower limit $\left( 45+15=60 \right)$ or subtract that value from upper limit $\left( 75-15=60 \right)$ to get the result.