1. **Stating the problem:** We want to create a fairer speeding fine system combining elements from New York and Massachusetts systems. 2. **Understanding the current systems:** - New York fines vary by speed over the limit with a minimum and maximum range. - Massachusetts fines have a flat charge for 1-10 mph over and a linear increase for 11-30 mph over. 3. **Goal:** Design a system that is fair, consistent, and easy to understand, balancing minimum fines and incremental increases. 4. **Proposed formula:** For speeds $s$ mph over the limit: - If $1 \leq s \leq 10$, fine = $\$75$ (a moderate flat charge between NY minimum and MA flat charge). - If $11 \leq s \leq 30$, fine = $75 + 15 \times (s - 10)$ (start at $75$, add $15$ per mph over 10). - If $s \geq 31$, fine = $375 + 20 \times (s - 30)$ (start at $375$, add $20$ per mph over 30). 5. **Explanation:** - The flat $75$ for 1-10 mph is fairer than NY's $45$ minimum and less than MA's $100$. - The $15$ per mph increment for 11-30 mph balances NY's $90$-$300$ range and MA's $10$ per mph. - For 31+ mph, a higher increment $20$ per mph reflects increased danger. 6. **Example calculations:** - For $s=5$, fine = $75$. - For $s=20$, fine = $75 + 15 \times (20-10) = 75 + 150 = 225$. - For $s=35$, fine = $375 + 20 \times (35-30) = 375 + 100 = 475$. 7. **Summary:** This system is simple, fair, and progressive, combining the best features of both states' systems.