Width of Rectangle Garden with Walkway

A rectangular garden is to be constructed with a length that is twice its width. The garden will be bordered by a walkway that is uniformly 3 feet wide on all sides. If the total area of the garden including the walkway is to be 800 square feet, what will be the width of the garden in feet?

Let the width of the garden be represented by $w$. Therefore, the length of the garden can be expressed as $2w$. The total dimensions of the garden including the walkway will be $(2w + 6)$ for the length and $(w + 6)$ for the width, since the walkway adds 3 feet on each side.

Set up the equation based on the total area: $$(2w + 6)(w + 6) = 800.$$