1. **State the problem:** Solve the equation $5(115 - n) = 3n - 17$ for $n$. 2. **Apply the distributive property:** Multiply 5 by each term inside the parentheses. $$5 \times 115 - 5 \times n = 3n - 17$$ which simplifies to $$575 - 5n = 3n - 17$$ 3. **Collect like terms:** Add $5n$ to both sides to move all $n$ terms to the right. $$575 - \cancel{5n} + 5n = 3n + 5n - 17$$ which simplifies to $$575 = 8n - 17$$ 4. **Isolate the term with $n$:** Add 17 to both sides. $$575 + 17 = 8n - 17 + 17$$ which simplifies to $$592 = 8n$$ 5. **Solve for $n$:** Divide both sides by 8. $$\frac{592}{\cancel{8}} = \frac{8n}{\cancel{8}}$$ which simplifies to $$n = 74$$ **Final answer:** $n = 74$