2460.11 – Angela's Age

Angela's age right now is exactly 3 times her age 3 years from now, minus 3 times her age 3 years ago. How old is Angela right now?

Solution

Let aa stand for Angela's age. Then her age 3 years from now will be a+3a + 3, and her age 3 years ago is a−3a - 3. So,

a=3(a+3)−3(a−3)=3a+9−(3a−9)=3a+9–3a+9=18\begin{aligned}a &= 3(a + 3) - 3(a - 3)\\&= 3a + 9 - (3a - 9)\\&= 3a + 9 – 3a + 9\\&= 18\end{aligned}

Check: If Angela is 18, then in 3 years she'll be 21, and 3 years ago she was 15.

So, does 18 equal 3×21−3×15=63−45=183 \times 21 - 3 \times 15 = 63 - 45 = 18? Yep.