Question

How old am I if 400 is reduced by twice my age is 244?

Answer 1

Hint: We will first represent the given statement as a linear equation. Then we will simplify it further using the basic mathematical operations to get the required answer. A linear equation is an equation that has the highest degree of 1 and has one solution.

Complete step-by-step answer:
We have to represent the given equation in a linear equation in one variable. Hence, we should know what exactly a linear equation in one variable means.
Hence, an equation is called a linear equation in one variable if it can be written in the form of $ax+b=0$ where $a,b$ are real numbers and $a\ne 0$, as it is the coefficient of $x$. Also, there is only one variable i.e. $x$ where, the power of this equation will also be 1 as it is a ‘linear equation’. And as a fun fact, a linear equation in one variable can have only one solution rather than infinitely many solutions in the case of ‘two variables’.
Now, according to the question,
Let the age of the person be $x$ years
Now, the question states that:
400 is reduced by twice the person’s age to get 244.
But as we have let the age of the person equal to $x$ years, hence, we can rewrite this sentence by substituting his age by $x$ years. Also, it is given that 400 is ‘reduced’ by twice the person’s age
Hence, we will subtract $2x$ from 400,
$400-2x$
Now, after subtracting twice his age from 400, we get 244, thus, this can be represented mathematically as:
$400-2x=244$
Subtracting 244 from both sides and adding $2x$ on both sides, we get,
$\Rightarrow 400-2x+2x-244=244-244+2x$
$\Rightarrow 400-244=2x$
Hence, we get,
$\Rightarrow 2x=156$
Dividing both sides by 2, we get
$\Rightarrow x=78$
Therefore, the age of the person is 78 years.

Hence, he is 78 years old if 400 reduced by twice his age is 244.
Thus, this is the required answer.

Note:
To answer this question we should know how to represent given information, mathematically. Also, understanding the meaning of the question plays an important role in such types of questions because if for example, we understood the meaning incorrectly then we could write the equation as $2x-400=244$, hence, making our equation completely wrong.
These small mistakes must be kept in mind and we should try to break the given question into parts and hence, make the required equation gradually.