Question

After $16$ years, Fatima will be thrice as old as she is now. Find her present age.

Answer 1

Hint: It is given that the relation between Fathima present age in now and after $16$ years. We have to find the age of Fathima at present. We are going to use a variable as a Fathima present age and convert the given relation into the linear transformations. By solving the linear transformation for variables we will get the Fathima age at present. Then we will find the final answer.

Complete step-by-step solution:
Here it is given the relation of age of Fathima. That is,
After $16$ years, Fatima will be thrice as old as she is now.
Consider the present age of Fathima as $x$ and equate the given condition accordingly to solve for $x$
Now,
Let us denote the present age of Fatima as $x$,
Then an age of Fatima after 16 years will be $ = x + 16$,
Now we substituting the linear term into the given relation we get,
After $16$ years, Fatima will be thrice as old as she is at present.
$ \Rightarrow 3\left( x \right) = x + 16$
Solving the terms for $x$,
$ \Rightarrow 3x - x = 16$
Subtracting the terms we get,
$ \Rightarrow 2x = 16$
Rearranging the terms,
$ \Rightarrow x = \dfrac{{16}}{2}$
Dividing the terms we get,
$ \Rightarrow x = 8$
Hence we get the value of the variable is $x = 8$
Since we take that variable $x$ as Fathima present age,
Hence the value of the variable $x$ is equal to Fathima age at present.

$\therefore $The present age of Fathima is $8$.

Note: In this problem, we consider the present age of Fathima with a variable so that it would be fine to apply some values to it. We can verify the answer by substituting the value of the variable in the equation. That is the value of $x = 8$ is substituted in the found equation we get $8 \times 3 = 24$ also $8 + 16 = 24$ that is the value of x we have found is absolutely correct. We use Linear equations in one variable if we have one unknown variable. We will use linear equations in two variables if there are two unknown variables.