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 (1)
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 they are $8 cheaper.
Explanation
Area of square tile First, let's calculate the area of each square tile. The tile is 2 1 foot by 2 1 foot, so the area is:
Calculating the area Area square = 2 1 foot × 2 1 foot = 4 1 square foot = 0.25 square foot
Number of square tiles Now, let's find out how many square tiles are needed to cover the 40 square foot bathroom floor.
Calculating the number of tiles Number square = Area square Floor Area = 0.25 square foot 40 square feet = 160 tiles
Cost of square tiles Next, we calculate the total cost of using the square tiles. Each square tile costs $0.45 .
Calculating the total cost Cost square = Number square × Cost per tile = 160 × $0.45 = $72.00
Area of rectangular tile Now, let's calculate the area of each rectangular tile. The tile is 2 feet by 4 1 foot, so the area is:
Calculating the area Area rectangular = 2 feet × 4 1 foot = 2 1 square foot = 0.5 square foot
Number of rectangular tiles Now, let's find out how many rectangular tiles are needed to cover the 40 square foot bathroom floor.
Calculating the number of tiles Number rectangular = Area rectangular Floor Area = 0.5 square foot 40 square feet = 80 tiles
Cost of rectangular tiles Next, we calculate the total cost of using the rectangular tiles. Each rectangular tile costs $0.80 .
Calculating the total cost Cost rectangular = Number rectangular × Cost per tile = 80 × $0.80 = $64.00
Comparing the costs Comparing the total costs, we have: Cost of square tiles: $72.00 Cost of rectangular tiles: $64.00
The rectangular tiles are cheaper.
Calculating the difference The difference in cost is:
Calculating the difference Difference = Cost square − Cost rectangular = $72.00 − $64.00 = $8.00
Final Answer Therefore, Orchid should choose the rectangular tiles because the total cost will be $8 less.
Examples
When tiling a floor, understanding the area of each tile and the total area to be covered helps in minimizing costs. This is similar to planning a garden where you need to calculate the area of flower beds and choose the most cost-effective plants to fill the space. By calculating the area and cost per unit, you can optimize your budget and make informed decisions, whether it's for tiling a bathroom or landscaping a garden.
