Final answer:
To cover the path around the square-shaped garden that is 11 feet wide with a surrounding path of 2 feet, we calculate the difference in area between the entire square and the garden itself and then determine how many bags of gravel are required based on the coverage of each bag. After calculations, it is determined that 9 bags are needed to cover the 72 square feet of the path.
Step-by-step explanation:
To calculate the number of bags of gravel needed to cover the path around the square-shaped vegetable garden, we first need to find the area of the path. The entire square (garden and path) is 11 feet wide, so the garden alone is 11 - 2 - 2 (subtracting the width of the path on both sides) which gives us 7 feet. The area of the garden is therefore 7 feet × 7 feet = 49 square feet.
To find the area of the entire square, we do 11 feet × 11 feet = 121 square feet. The area of the path will be the area of the entire square minus the area of the garden: 121 square feet - 49 square feet = 72 square feet.
Since one bag of gravel covers 8 square feet, we divide the area of the path by the coverage of one bag: 72 square feet ÷ 8 square feet/bag = 9 bags. Therefore, 9 bags of gravel are needed to cover the path.