Finding Path Width Around Garden

A rectangular garden measures 12 meters in length and 8 meters in width. The owner wants to add a path of uniform width around the garden. If the total area of the garden and the path combined is to be 220 square meters, what should be the width of the path?

Let the width of the path be denoted as $x$ meters. The area of the garden itself is $12 \times 8 = 96$ square meters. The dimensions of the entire area, including the path, will then be:

Length: $12 + 2x$ meters

Width: $8 + 2x$ meters

The combined area, therefore, can be expressed as:

$$ A = (12 + 2x)(8 + 2x) $$

Set the equation for the total area equal to 220 square meters:

$$ (12 + 2x)(8 + 2x) = 220 $$