Question

In 34 years, John will be three times as old as he is now. Find his present age.

Answer 1

Hint: Here, we need to find the present age of John. We will assume the present age of John to be \[x\] years. We will use the given information to form a linear equation. Then, we will solve this linear equation to get the value of \[x\], and hence, the present age of John.

Complete step-by-step answer:
We will form a linear equation in one variable using the given information and solve it to find the present age of John.
We will assume that the present age of John be \[x\] years.
The age of John 34 years later will be 34 more than his present age.
Thus, we get the age of John 34 years later as \[x + 34\] years.
Now, it is given that the age of John 34 years later is three times his present age.
Thus, we get the linear equation
\[x + 34 = 3x\]
Now, we will solve this linear equation to find the value of \[x\], and hence, the present age of John.
Subtracting \[x\] from both sides, we get
\[ \Rightarrow x + 34 - x = 3x - x\]
Thus, we get
\[ \Rightarrow 34 = 2x\]
Dividing both sides by 2, we get
\[ \Rightarrow \dfrac{{34}}{2} = \dfrac{{2x}}{2}\]
Therefore, we get the value of \[x\] as
\[ \Rightarrow x = 17\]
\[\therefore \] The present age of John is 17 years.

Note: We have formed a linear equation in one variable using the given information. A linear equation in one variable is an equation of the form \[ax + b = 0\], where \[a\] is not equal to 0, and \[a\] and \[b\] are real numbers. For example, \[x - 100 = 0\] and \[100x - 566 = 0\] are linear equations in one variable \[x\].
We can verify the answer by using the given information.
John’s age 34 years later will be \[17 + 34 = 51\] years.
We know that \[17 \times 3 = 51\].
Therefore, we have verified that the age of John 34 years later will be three times his present age.