Orchid wants to retile her bathroom floor, which has an area of 40 square feet. She is deciding between two types of custom tiles. The square tile is [tex]$\frac{1}{2}$[/tex] foot by [tex]$\frac{1}{2}$[/tex] foot and costs $0.45 per tile. The rectangular tile is 2 feet by [tex]$\frac{1}{4}$[/tex] foot and costs $0.80 per tile.
Which tile should Orchid choose to minimize costs? Explain.
A. She should choose the square tiles because the total cost will be $8 less.
B. She should choose the rectangular tiles because the total cost will be $8 less.
C. She should choose the square tiles because the total cost will be $14 less.
D. She should choose the rectangular tiles because the total cost will be $14 less.
Answer (2)
Calculate the area of the square tile: 2 1 × 2 1 = 0.25 square feet.
Determine the number of square tiles needed: 0.25 40 = 160 tiles, costing 160 × $0.45 = $72 .
Calculate the area of the rectangular tile: 2 × 4 1 = 0.5 square feet.
Determine the number of rectangular tiles needed: 0.5 40 = 80 tiles, costing 80 × $0.80 = $64 . Therefore, Orchid should choose the rectangular tiles because the total cost will be $8 less.
Explanation
Problem Analysis First, let's analyze the problem. Orchid needs to retile her bathroom floor and wants to choose the tile that minimizes the cost. We have two options: square tiles and rectangular tiles. We need to calculate the total cost for each type of tile and then compare them.
Area of Square Tile Let's calculate the area of the square tile. The square tile is 2 1 foot by 2 1 foot, so its area is: 2 1 × 2 1 = 4 1 = 0.25 square feet
Number of Square Tiles Now, let's find out how many square tiles are needed to cover the 40 square feet floor. We divide the total area by the area of one square tile: 0.25 40 = 160 tiles
Total Cost of Square Tiles The cost of each square tile is $0.45 . So, the total cost of using square tiles is: 160 × $0.45 = $72
Area of Rectangular Tile Next, let's calculate the area of the rectangular tile. The rectangular tile is 2 feet by 4 1 foot, so its area is: 2 × 4 1 = 4 2 = 2 1 = 0.5 square feet
Number of Rectangular Tiles Now, let's find out how many rectangular tiles are needed to cover the 40 square feet floor. We divide the total area by the area of one rectangular tile: 0.5 40 = 80 tiles
Total Cost of Rectangular Tiles The cost of each rectangular tile is $0.80 . So, the total cost of using rectangular tiles is: 80 × $0.80 = $64
Comparison and Conclusion Comparing the total costs, the square tiles cost $72 and the rectangular tiles cost $64 . Therefore, the rectangular tiles are cheaper.
To find the difference in cost: $72 − $64 = $8
The rectangular tiles are $8 cheaper than the square tiles.
Examples
When planning a garden, you might need to cover a certain area with paving stones. By calculating the area of each paving stone and the total area to be covered, you can determine the number of stones needed and compare the costs from different suppliers to minimize expenses, just like Orchid choosing the cheaper tiles for her bathroom floor.
Orchid should choose the rectangular tiles, as they cost $64 compared to the $72 for square tiles, making the rectangular tiles $8 cheaper. Therefore, the correct option is B.
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