Question

A square deck is 6 ft long and 6 ft wide. Ravi would like to use pebbles to cover the deck. The coverage of each sheet of pebbles is measured in square inches.

(a) Find the area of the deck in square inches.
b) Ravi wants to cover the deck with pebbles. He doesn't have any to begin with and he can't buy partial sheets of pebbles. Each sheet of pebbles covers 134 square inches. How many whole sheets of pebbles will he need to buy in order to completely cover the deck?
c) If each sheet of pebbles costs $9.50, how much will Ravi need to spend on pebbles?

Answer 1

The area of the square deck is 5184 square inches. Ravi will need to purchase 39 whole sheets of pebbles to cover the deck. The total cost for the pebbles will be $370.50.

Step-by-step explanation:

The student's question involves the calculation of the area of a square deck, determining the number of pebble sheets needed to cover that area, and calculating the total cost of the pebble sheets.

Part A: Calculating the Area of the Deck

First, we need to find the area of the deck in square inches. Since the deck is a square with each side measuring 6 ft, we convert feet to inches by multiplying by 12 (since 1 foot = 12 inches).

6 ft × 12 in/ft = 72 inches.

Therefore, the area of the deck is 72 in × 72 in = 5184 square inches.

Part B: Determining the Number of Pebble Sheets

Each sheet covers 134 square inches, so we divide the total area by 134 to find the number of sheets:

5184 sq in / 134 sq in/sheet = 38.7 sheets.

Since Ravi cannot buy partial sheets, he would need to purchase 39 sheets to cover the deck completely.

Part C: Calculating the Total Cost

Each sheet costs $9.50; thus:
39 sheets × $9.50/sheet = $370.50

Therefore, Ravi will need to spend $370.50 on pebble sheets to cover his deck.