Laurence is painting the walls and ceiling of a rectangular bedroom that is 5 m by 6.5 m. The walls are 2.5 m high.There is a window measuring 1 m by 0.8 m on one wall and a door that is 1 m by 2.3 m in another wall.If a can of paint covers 20 m2 and costs $38.95, what will it cost Laurence for paint for this bedroom?
Question
Laurence is painting the walls and ceiling of a rectangular bedroom that is 5 m by 6.5 m. The walls are 2.5 m high.There is a window measuring 1 m by 0.8 m on one wall and a door that is 1 m by 2.3 m in another wall.If a can of paint covers 20 m2 and costs $38.95, what will it cost Laurence for paint for this bedroom?
Solution
First, we need to calculate the total area that Laurence needs to paint.
The area of the four walls is calculated by adding the area of each wall. Since the room is rectangular, opposite walls are equal. So, we have two walls of 5m by 2.5m and two walls of 6.5m by 2.5m.
Area of smaller walls = 2 * (5m * 2.5m) = 25 m² Area of larger walls = 2 * (6.5m * 2.5m) = 32.5 m²
So, the total area of the walls is 25 m² + 32.5 m² = 57.5 m².
Next, we need to subtract the area of the door and the window from the total area of the walls, because Laurence won't paint them.
Area of the door = 1m * 2.3m = 2.3 m² Area of the window = 1m * 0.8m = 0.8 m²
So, the total area that Laurence won't paint is 2.3 m² + 0.8 m² = 3.1 m².
Therefore, the total area that Laurence needs to paint is 57.5 m² - 3.1 m² = 54.4 m².
Finally, we need to calculate the cost of the paint. Since one can of paint covers 20 m², Laurence will need 54.4 m² / 20 m²/can = 2.72 cans of paint. Since he can't buy a fraction of a can, he'll need to buy 3 cans.
So, the total cost for the paint will be 3 cans * 116.85.
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