The sum of the present ages of a mother and her son is $42$. What was the mother's age $15$ years ago before her son was born? > The sum of the present ages of a mother and her son is $42$. When the mother was same age as her son now, her son wouldn't be born until $15$ years later. What was the mother's age when her son was born? This question had seemed a bit complex. However, we can say that $$M + S = 42 \tag {1}$$ where $M = \text{Mother}$, $S = \text{Son}$ > Mother's age $15$ years ago before her son was born $$ M-t = -S-15 \tag{2}$$ $$t = \text{passed time}$$ This is where I'm stuck. I'll be waiting for your professional helps.

We have $M+S=42$, assume that the mother is $t$ years older than her son.

Currently, the mother is $M$ years old and the son is $S$ years old.

$\Rightarrow$ $t$ years ago, the mother was $M-t=S$ years old and her son was $S-t$ years old. Note that the son wouldn't be given birth until $15$ years later, so at this point we consider that her son was $-15$ years old or $S-t=-15$.

We have this set of equations:

$${\begin{cases}M+S=42\\\M-S-t=0\\\S-t=-15\end{cases}}$$

After solving this, you can check the answer below.

> The mother is currently $33$ years old, the son is currently $9$ years old.