John wants to put a circular garden in his back yard. The garden has a diameter of 16 feet. He needs to cover the garden with peat moss. Each bag of peat moss can cover 90 square feet. How many bags does he need?

The area of John's back yard garden will be A = pi*r^2 where r = radius = 1/2 the diameter.

Then set up a proportion as follows:
(1 bag/90 ft^2)=(x bags/area garden)
solve for x bags. The answer I obtained is 2.23 bags; therefore, John must buy 3 bags.

To find out how many bags of peat moss John needs to cover the circular garden, we first have to calculate the area of the garden. We know that the garden has a diameter of 16 feet, so we can find the radius by dividing the diameter by 2.

Radius = Diameter / 2 = 16 feet / 2 = 8 feet

Next, we need to calculate the area of the circular garden using the formula for the area of a circle:

Area = π * radius^2

We can estimate π to be approximately 3.14:

Area = 3.14 * (8 feet)^2 = 3.14 * 64 square feet = 200.96 square feet

Since each bag of peat moss can cover 90 square feet, we divide the area of the garden by the coverage of each bag to find the number of bags John needs:

Number of bags = Area / Coverage per bag

Number of bags = 200.96 square feet / 90 square feet ≈ 2.23 bags

Therefore, John will need approximately 2.23 bags of peat moss. Since he cannot purchase a fraction of a bag, he will need to round up to the nearest whole number.

John needs 3 bags of peat moss to cover the circular garden.