Question

If $86$ exceeds another number by $9$. What is the other number?

Answer 1

Hint: Consider the number as a variable and let the number be x. Then, write the equation with the help of data given in the question. We will then use the method of transposition to shift the terms from one side of the equation to the other and find the value of x.

Complete step-by-step answer:
If you find these types of questions, you must know to pick up the numbers which are given in the question. The numbers which are given in the question are eighty six $\left( {86} \right)$, variable (let's suppose it to be x) and nine $\left( 9 \right)$. Now, we have to use the hint given in the language of the question to arrange all these numbers in an equation. We have to divide the sentence into two comparatively smaller phrases. The small phrases are “eighty six exceeds the number” and “by nine”.
Interpreting the data and rewriting it in the form of a mathematical equation, we can infer that $\left( {86} \right)$ is greater than the variable x by $\left( 9 \right)$. So, we get,
$ \Rightarrow 86 - x = 9$
Now, using a method of transposition to shift the terms in the equation and isolating the variable. So, we add number x to both the sides of equation,
$ \Rightarrow 86 - x + x = 9 + x$
Cancelling similar terms with opposite signs,
$ \Rightarrow 86 = 9 + x$
Shifting all constants to one side of equation,
$ \Rightarrow x = 86 - 9$
Simplifying the calculation,
$ \Rightarrow x = 77$
So, the correct answer is “77”.

Note: Expressions are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between. The mathematical operators can be of addition, subtraction, multiplication, or division. Here in the given example it is a linear equation in one variable and since it is linear it will have only one solution.