Planting trees along a straight road: Find the maximum number of trees that can be planted 20 m apart on both sides of a straight road 1760 m long, including trees at both ends.

Introduction / Context:
Spacing problems rely on the spacing formula: when placing items at fixed intervals along a segment and including both ends, the count on one side is (length/spacing) + 1. For two sides, double that number. Careful inclusion of endpoints is crucial.

Given Data / Assumptions:

• Road length L = 1760 m.
• Spacing = 20 m.
• Trees are placed on both sides; endpoints are included.

Concept / Approach:
For one side: count = L/spacing + 1. Then multiply by 2 for both sides. Do not double-count endpoints across sides because each side is independent.

Step-by-Step Solution:
One-side count: 1760 / 20 + 1 = 88 + 1 = 89.Both sides: 2 * 89 = 178.Therefore, the maximum number of trees is 178.

Verification / Alternative check:
Reverse reasoning: If there are 89 trees on one side, there are 88 intervals (88 * 20 = 1760 m), confirming the formula.

Why Other Options Are Wrong:
174 and 176 undercount by missing endpoints; 180 overcounts by adding extra positions; 172 undercounts more severely.

Common Pitfalls:
Using L/spacing instead of L/spacing + 1; forgetting to multiply by 2 for both sides; assuming shared endpoints reduce the total (they do not across different sides).

Final Answer:
178