The sum of the current ages of Ahmad and Henry is $54$.

Question

The sum of the current ages of Ahmad and Henry is $54$. When Ahmad were the same age as Henry's current age, Henry was $18$. What is Ahmad's current age?

Here is what I thought

$A + H = 54$

$A-t = H, H = 18$

$t$ = passed time

I can't think anyhing more. Can I get your thinkings?

Answer 1

$$A + H = 54$$ $$A-t = H$$ $$H-t=18$$ Three equations, three unknowns.

Answer 2

Currently, Ahmad is $A$ years old, Henry is $H$ years old ($A+H=54$).

$H$ years later from now, Ahmad will be $A+H$ years old, Henry will be $2H$ years old.

$H-A$ years later from now, Ahmad will be $H$ years old, Henry will be $2H-A$ years old. The task indicated that when Ahmad was $H$ years old, Henry was $18$ years old, so:

$$2H-A=18$$

We have this set of equations:

${\begin{cases}A+H=54\\2H-A=18\end{cases}\Rightarrow {\begin{cases}A=30\\H=24\end{cases}}}$