3. A woman is 32 years older than her son. Ten years ago, she was three times as old as her son was at that time. Find the current age of the woman and her son.

Let's use some algebra to solve this age puzzle! Let the current age of the son be \( x \) years. Then, the woman's current age would be \( x + 32 \). According to the problem, ten years ago, the woman was \( x + 32 - 10 = x + 22 \), and the son was \( x - 10 \). At that time, the woman’s age was three times the son’s age: \[ x + 22 = 3(x - 10) \] \[ x + 22 = 3x - 30 \] \[ 22 + 30 = 3x - x \] \[ 52 = 2x \] \[ x = 26 \] So, the son is currently 26 years old, and the woman, being 32 years older, is \( 26 + 32 = 58 \) years old. Therefore, the woman is 58 years old, and her son is 26 years old! Fun fact: Challenges like this one often pop up in math competitions, making them a great way to sharpen your problem-solving skills while having a little fun! To avoid common mistakes when working with age problems, always ensure you're setting your variables correctly and double-check the equations you form. Misplacing a number or misinterpreting "ten years ago" can lead you down the wrong path!