Question

If $11$ is subtracted from $4$ times a number, the result is $89$. Find the number.

Answer 1

Hint: We will first formulate an algebraic equation using the information given to us in the question. Consider the number as a variable and let the number be x. Then, write the equation with the help of the language and hints, which is given in the question. Then, we will solve the equation using the method of transposition.

Complete step by step answer:
We need to be clear with the language of the question and understand the question properly.
If you find these types of question, you must know to pick up the numbers which are given in the question. The numbers which are given in the question are eleven$\left( {11} \right)$, variable (lets suppose it to be x) and eighty nine $\left( {89} \right)$.
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 “eleven is subtracted from”, “four-time a number” and “is equal to eighty-nine”.
Interpreting the data and rewriting it in form of a mathematical equation, we get,
$4x - 11 = 89$
Adding $11$ to both sides of the equation, we get,
$ \Rightarrow 4x - 11 + 11 = 89 + 11$
Cancelling the like terms with opposite signs, we get,
$ \Rightarrow 4x = 89 + 11$
On further simplification, we get,
$ \Rightarrow 4x = 100$
Dividing both the sides of equation by $4$, we get,
$ \Rightarrow x = \dfrac{{100}}{4} = 25$
So, the value of x is $25$.
Hence, the number is $25$.

Note:
There are three methods to solve linear equations in one variable.
1. Trial and Error.
2. Inverse operations.
3. Transposition Method.