[Number Theory]
Problem: Let $p$ be a prime number. If $p$ years ago, the ages of three children formed a geometric sequence with a sum of $p$ and a common ratio of 2 , compute the sum of the children's current ages.

Solution: Let $x, 2 x$, and $4 x$ be the ages of the children $p$ years ago. Then $x+2 x+4 x=p$, so $7 x=p$. Since $p$ is prime, $x=1$. Thus the sum of the children's current ages is $(1+7)+(2+7)+(4+7)=\mathbf{2 8}$.

Final answer: 28