One gallon of floor paint costs $22.99 and can cover a 20-foot by 20-foot floor. How much would the floor paint cost to paint a 60-foot by 60-foot floor?
Answer (2)
Calculate the area covered by one gallon of paint: 20 ft × 20 ft = 400 ft 2 .
Calculate the area of the floor to be painted: 60 ft × 60 ft = 3600 ft 2 .
Calculate the number of gallons needed: 400 3600 = 9 gallons.
Calculate the total cost: 9 × $22.99 = $206.91 . The total cost is $206.91 .
Explanation
Problem Analysis We are given that one gallon of floor paint costs $22.99 and covers a 20-foot by 20-foot floor. We need to find the cost to paint a 60-foot by 60-foot floor.
Area Covered by One Gallon First, let's find the area that one gallon of paint covers. The area is given by: 20 ft × 20 ft = 400 ft 2 So, one gallon covers 400 square feet.
Area of the Floor to be Painted Next, let's find the area of the floor we need to paint. The area is given by: 60 ft × 60 ft = 3600 ft 2 So, the floor to be painted has an area of 3600 square feet.
Number of Gallons Needed Now, we need to find out how many gallons of paint are needed. We divide the total area to be painted by the area covered by one gallon: 400 ft 2 / gallon 3600 ft 2 = 9 gallons So, we need 9 gallons of paint.
Total Cost Finally, we calculate the total cost by multiplying the number of gallons needed by the cost per gallon: 9 gallons × $22.99/ gallon = $206.91 Therefore, the total cost to paint the floor is $206.91.
Examples
When planning a home renovation, calculating paint costs is essential for budgeting. This problem demonstrates how to determine the amount of paint needed and the total expense, ensuring you don't overspend. Understanding area calculations and proportional costs helps in various real-life scenarios, such as tiling a bathroom, carpeting a room, or even estimating the cost of materials for a construction project. By mastering these calculations, you can make informed decisions and manage your resources effectively.
To paint a 60-foot by 60-foot floor, you will need 9 gallons of paint, costing a total of $206.91. Each gallon covers 400 square feet, and the total area to be painted is 3600 square feet. Thus, the calculations show how to determine both the amount of paint needed and the total cost involved.
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