Width of a Garden Pathway

A rectangular garden measures 20 meters in length and 15 meters in width. A pathway of uniform width is constructed around the garden. If the total area of the garden and the pathway together is 600 square meters, what is the width of the pathway?

Let the width of the pathway be denoted as $w$.

To solve this, calculate the area of the larger rectangle (the garden plus pathway) and set it equal to 600 square meters. The dimensions of the larger rectangle will be $(20 + 2w)$ meters in length and $(15 + 2w)$ meters in width.

The area of the larger rectangle can be calculated as:

$$A = (20 + 2w)(15 + 2w)$$

Solve for $w$ such that:

$$A = 600$$