#### Answer

Dudley is $3x+1$ years old.

#### Work Step by Step

Starting at Jack's age, $x$, we must first multiply by $3$ because it says "$3$ times as old as Jack," giving us $3x$. We must then add $1$ to this product to arrive at Dudley's age, for it says that Dudley's age is $1$ more than this product. This gives us $3x+1$.