Age word problem

Question

Adam is now one quarter of his father's age and in $5$ years time, his age will be one-third the age of his father. How old is Adam now?

I have trouble with these kind of questions and I've spent half an hour trying to figure it out but I still don't know how to get the answer D:

Answer 1

Let $x$ be Adam's current age, and let $y$ be his father's current age. The statement

Adam is now one quarter of his father's age

means $$x=\frac{1}{4}y,$$ and the statement

in 5 years time, his age will be one third the age of his father

means $$(x+5)=\frac{1}{3}(y+5),$$ because in $5$ years, Adam's age will be $x+5$, and his father's age will be $y+5$.

So, you have the system of equations $$\begin{align*} x&=\frac{1}{4}y\\\\\\\\ (x+5)&=\frac{1}{3}(y+5) \end{align*}$$ which can be rewritten as $$\begin{align*} 4x&=y\\\\\\\ 3x+15&=y+5 \end{align*}$$ and then further rewritten as $$\begin{align*} 4x-y&=0\\\\\\\ 3x-y&=-10 \end{align*}$$ Do you know how to proceed from here?

Answer 2

Let Adam's current age be $x$ years so that the current age of his father is $4x$ years

According to the given condition $x+5=\frac{4x+5}3\implies 4x+5=3x+15\implies x=10$