Question

After 15 years, Mary’s age will be 4 times her present age. Find her present age.

Answer 1

Hint: Here, we will assume Mary’s age to be \[x\]. We will find Mary’s age after 15 years in terms of \[x\] and calculate 4 times Mary’s age. We will equate the 2 expressions and form a linear equation. We will solve the linear equation to find the value of $x$. The result will be the required answer to the question.

Complete step-by-step answer:
We will assume that the present age of Mary is \[x\] years.
We will write the equation for Mary’s age after 15 years. It will be the sum of 15 and \[x\]:
\[{\rm{Age}} = x + 15\]
We know that after 15 years Mary’s age will be 4 times her present age. Therefore, we get
\[x + 15 = 4x\]
Subtracting \[x\] from both sides, we get
\[ \Rightarrow x + 15 - x = 4x - x\]
We will collect the like terms on both sides of the above equation. Therefore, we get
\[ \Rightarrow \left( {x - x} \right) + 15 = \left( {4x - x} \right)\]
Simplifying the above equation, we get
\[\begin{array}{l} \Rightarrow 0 + 15 = 3x\\ \Rightarrow 15 = 3x\end{array}\]
Dividing both sides by 3, we get
\[ \Rightarrow \dfrac{{15}}{3} = \dfrac{{3x}}{3}\]
We know that 15 divided by 3 is equal to 5 and 3 divided by 3 is equal to 1. We will substitute these values in the above equation and further simplify it. Therefore, we get
\[ \Rightarrow 5 = x\]
We have calculated the value of \[x\] to be 5.
So, the present age of Mary is 5 years.

Note: We can also take Mary’s age after 15 years to be \[x\]. So, Mary’s current age will be
\[x - 15\] years.
Her age after 15 years is 4 times her current age:
\[\begin{array}{l}x = 4\left( {x - 15} \right)\\ \Rightarrow x = 4x - 60\end{array}\]
Subtracting the like terms, we get
\[\begin{array}{l} \Rightarrow 60 = 3x\\ \Rightarrow 20 = x\end{array}\]
So, her present age will be:
\[\begin{array}{l}x - 15 = 20 - 15\\ \Rightarrow x - 15 = 5{\rm{ years}}\end{array}\]