Final answer:
To calculate the total cost for the paint, we need to determine the total area of the walls and ceiling. We convert the measurements to feet and calculate the wall and ceiling areas. Then, we divide the total area by the coverage per gallon to find the number of gallons needed. Finally, we multiply the number of gallons by the cost per gallon to find the total cost. The total cost for the paint is $39.58 (excluding tax).
Step-by-step explanation:
To solve this problem, we need to calculate the total area of the walls and ceiling, and then determine how many gallons of paint are needed. We start by converting the measurements to the same unit: feet.
The room measures 20 feet by 13.5 feet, and the ceiling is 9 feet high. The door opening is 36 inches by 8 feet, and the window is 20 inches by 60 inches.
To calculate the wall area, we multiply the perimeter by the height.
The perimeter is (20 + 13.5) x 2 = 67 feet. The window area is 20 inches by 60 inches, which converts to
(20/12) x (60/12) = 10 x 5 = 50 square feet.
So, the total wall area is 67 x 9 - 50 = 603 square feet.
The ceiling area is 20 x 13.5 = 270 square feet.
To determine the total area, we add the wall area and ceiling area: 603 + 270 = 873 square feet.
Since each gallon of paint covers 400 square feet, we divide the total area by 400 to find the number of gallons needed: 873/400 = 2.183.
Round this up to the nearest tenth, and we need 2.2 gallons of paint.
Finally, to find the total cost, we multiply the number of gallons needed by the cost per gallon:
2.2 x 17.99 = $39.58.
Therefore, the total cost for the paint is $39.58 (excluding tax).