1. **State the problem:** Solve the proportion $$\frac{3}{14} = \frac{15}{m-3}$$ for $m$. 2. **Use the cross-multiplication formula:** For proportions $\frac{a}{b} = \frac{c}{d}$, cross multiply to get $a \times d = b \times c$. 3. **Apply cross multiplication:** $$3 \times (m-3) = 14 \times 15$$ 4. **Simplify both sides:** $$3(m-3) = 210$$ 5. **Distribute 3 on the left side:** $$3m - 9 = 210$$ 6. **Add 9 to both sides:** $$3m - 9 + 9 = 210 + 9$$ $$3m = 219$$ 7. **Divide both sides by 3:** $$\frac{\cancel{3}m}{\cancel{3}} = \frac{219}{3}$$ $$m = 73$$ **Final answer:** $m = 73$