2460.29 – Present and Future Ages II

Alfie is 5 years old. His mother is 28. How old will Alfie be when he is exactly half as old as his mother?

Solution

Let $x$ be the number of years until Alfie is half as old as his mom; then $5 + x = \dfrac{28 + x}{2}$ , or $2(5 + x) = 28 + x$ . A few more steps and we find that $x = 28 – 10 = 18$ .

In 18 more years Alfie will be half the age of his mother. Alfie will be $5 + 18 = 23$ . His mom will be $28 + 18 = 46$ . Put another way: She was 23 when he was born. So she's 23 years older. She'll be 46 when he's 23.