Question

How do you define your variables when given a word problem?

Answer 1

Hint: For defining the variables when given a word problem, Firstly we will have to read the word problem carefully and find out what is about to solve. After that we will assume that part which will have to find the word problem in a variable so that the problem will be easy to solve.

Complete step by step answer:
A word problem is also a mathematical problem that is in the form of sentences, stories or scenarios in which all the given data is described.
Since, it is in the form of stories or scenarios. We will read it carefully and have to figure out that part of the problem that is about to find the value. Here, we will try to understand the method by an example related to word problem as:
For example: A father is three times his son. After ten years he will become two times the son. What is the age of the son?
Since, the given problem is in the format of sentences. We will read it carefully and find out what the questions in the given world problem have. Here, we will have to find the age of the son.
So, we will assume it as:
Let us consider the age of the son be . So $x$ is the variable in a given word problem.
After that we will make an equation with the help of the one sentence according to the question as:\[\Rightarrow \text{Age of the father }=\text{ 3}\times \text{Age of the son}\]
Since, we will assume the age of son as $x$, we can write the above equation as:
\[\Rightarrow \text{Age of the father }=\text{ 3}\times x\]
\[\Rightarrow \text{Age of the father }=\text{ 3}x\]
Here, we will make another equation with the help of the sentence according to the question as:
\[\Rightarrow \text{Age of the father after ten years }=\text{ 2}\times \text{Age of the son after ten years}\]
Since, from the previous equation, we got the age of the father and we already assumed the age of the son. So, we can write the above equation as:
$\Rightarrow 3x+10=2\left( x+10 \right)$
Now, we will simplify the above equation by opening bracket as:
$\Rightarrow 3x+10=2x+20$
Now, we will make exchange the place to combine equal like terms as:
$\Rightarrow 3x-2x=20-10$
$\Rightarrow x=10$
Hence, the age of the son is $10$years old.

Note:
For defining the variables when given a word problem, we will consider the variable whatever the question is asked. As for the example: in the above example question, we assumed the age of the son as $x$ and got the value of the variable $10$ . Now, we can verify that the value of the variable is correct or not in the way as:
Since, the example there is a sentence that after ten years the age of the father is two times the age of the son. So, the equation will be:
$\Rightarrow 3x+10=2\left( x+10 \right)$
We will put the value of variable in the equation to verify it as:
L.H.S.-
$\Rightarrow 3x+10$
$\Rightarrow 3\times 10+10$
$\Rightarrow 30+10$
$\Rightarrow 40$
R.H.S.-
$\Rightarrow 2\left( x+10 \right)$
$\Rightarrow 2\left( 10+10 \right)$
$\Rightarrow 2\times 20$
$\Rightarrow 40$
Since, L.H.S. is equal to R.H.S. Hence, the variable for a given word problem is clearly derived.