Question

Nine times a number diminished by \[4\] , is \[95\] . How do you find the number?

Answer 1

Hint: This question involves the arithmetic operations like addition/ subtraction/ multiplication/ division. We need to know the keyword diminished indicates (it refers to subtraction) which operation. The final answer would satisfy all given conditions in the given problem. Also, we need to know how to convert the fraction term into whole number terms.

Complete step-by-step answer:
In the given question we would find the number which satisfies the condition nine times a number, diminished by \[4\] , is \[95\] .
Here we take the number as \[n\] .
Nine times a number can be written as \[9n\] diminished indicates the arithmetic operation subtraction.
So, we get diminished by \[4\] is \[9n - 4\] .
They told,
Nine times a number diminished by \[4\] , \[9n - 4\] is \[95\] . So, we get
 \[9n - 4 = 95\]
Let’s move the term \[ - 4\] from LHS to RHS of the above equation, we get
 \[9n = 95 + 4\]
By solving the above equation we get
 \[9n = 99\]
Let’s move the term \[9\] from LHS to RHS of the above equation we get,
 \[n = \dfrac{{99}}{9}\]
 $ n=11 $
So, the correct answer is “ $ n=11 $”.

Note: The given question describes the arithmetic operation of addition/ subtraction/ multiplication/ division. Note that when we move any one term from the left-hand side to the right-hand side or right-hand side to the left-hand side of the equation the arithmetic operation operations can be modified as given below,
The addition process is converted into a subtraction process.
The subtraction process is converted into an additional process.
The multiplication process is converted into a division process.
The division process is converted into the multiplication process.