Question

The difference of $9$ times a number and $2$ is $67,$ how do you find the number?

Answer 1

Hint: We will first convert the words in the given statement into the Mathematical counterparts. We will find out the operation mentioned in the given statement. Then, we will apply the operation on the terms we obtain.

Complete step by step solution:
Let us consider the given statement, the difference of $9$ times a number and $2$ is $67.$
We are asked to find the unknown number in the statement for which the difference is $67.$
Let us suppose the number to be found is $x.$
To find the value of the number $x,$ we need to change the given statement into its Mathematical counterpart and do the operations mentioned.
We know that the word ‘times’ implies the multiplication.
Also, we know that the word difference means the subtraction.
So, in the given statement, we can see that there are two operations in the given statement.
The first operation is multiplication of $9$ with the number $x.$
We will get, $9x.$
The second operation is subtraction of $2$ from the product we have obtained, $9x.$
Now, we will get, $9x-2.$
It is given that the difference is $67.$
Since the difference is $67,$ we can equate it with the above Mathematical expression we have found.
So, we will get $9x-2=67.$
Let us transpose $2$ from the left-hand side of the equation to the right-hand side to get $9x=67+2=69.$
Now, we will transpose $9$ from the left-hand side to the right-hand side to get $x=\dfrac{69}{9}.$
We can simplify it further by dividing both the numerator and the denominator with $3$ to get $x=\dfrac{23}{3}.$

Hence the number is $x=\dfrac{23}{3}.$

Note: We can solve all the problems easily if it is converted to Mathematical form. The obtained fraction can be written in the decimal form, $x=7.667.$