Step 1 :Given: When 16 is subtracted from half of the number $r$, the result is at most 18.
Step 2 :Write this as an inequality: \(\frac{r}{2} - 16 \leq 18\)
Step 3 :Solve the inequality for $r$: \(\frac{r}{2} \leq 34\)
Step 4 :Final Answer: \(\boxed{r \leq 68}\)