Question

A number is such that it is as much greater than $ 65 $ as it is less than $ 91 $ . Find the number.

Answer 1

Hint: Since the number is as much greater than $ 65 $ as it is less than $ 91 $ so that means the difference between number and $ 65 $ will be equal to the difference between number and $ 91 $ .
Given data:
The number is as much greater than $ 65 $
As it is less than $ 91 $

Complete step-by-step answer:
Let the number be $ x $
So the difference between number and $ 65 $ will be
 $ x - 65 $
And the difference between number and $ 91 $ will be
 $ 91 - x $
These two differences will be equal
 $\Rightarrow x - 65 = 91 - x $
Further solving this equation
 $
 x + x = 91 + 65 \\
 2x = 156 \\
 x = 156/2 \\
 x = 78 \\
    \\
 $
Thus $ 78 $ is as much greater than $ 65 $ as it is less than $ 91 $ . So the number will be $ 78 $ .

Note: The average of two numbers is as much greater than one number as it is less than another number.
when numbers and variables are moved from right-hand side to left-hand side and vice versa then the sign of numbers and variables get changed. Minus converted into plus and minus, similarly multiply into divide and divide into multiply.