1. **State the problem:** We need to find a number such that when $\frac{3}{4}$ of it is added to 9, the result is 27. 2. **Set up the equation:** Let the number be $x$. The problem translates to: $$\frac{3}{4}x + 9 = 27$$ 3. **Isolate the term with $x$:** Subtract 9 from both sides: $$\frac{3}{4}x + 9 - 9 = 27 - 9$$ $$\frac{3}{4}x = 18$$ 4. **Solve for $x$:** Multiply both sides by the reciprocal of $\frac{3}{4}$, which is $\frac{4}{3}$: $$x = 18 \times \frac{4}{3}$$ 5. **Simplify:** $$x = \cancel{18} \times \frac{4}{\cancel{3}} = 6 \times 4 = 24$$ 6. **Answer:** The number is $\boxed{24}$.