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 1 2 \frac{1}{2} 2 1 Foot By 1 2 \frac{1}{2} 2 1 Foot And Costs $0.45 Per Tile.The Rectangular
Introduction
Orchid is faced with a common dilemma when it comes to renovating her bathroom floor. With an area of 40 square feet, she needs to decide between two types of custom tiles: square and rectangular. In this article, we will delve into the mathematical analysis of these two options, considering factors such as tile size, cost, and coverage area.
The Square Tile Option
The square tile is foot by foot, making it a compact and efficient choice for covering a small area like a bathroom floor. With a cost of $0.45 per tile, Orchid needs to calculate the total number of tiles required to cover the 40 square foot area.
Calculating the Number of Square Tiles Required
To calculate the number of square tiles required, we need to divide the total area of the bathroom floor (40 square feet) by the area of a single square tile ( foot by foot).
import math
total_area = 40 # square feet
tile_size = 0.5 # foot
num_tiles = total_area / (tile_size ** 2)
print(num_tiles)
Running this code, we get:
num_tiles = 400
So, Orchid would need 400 square tiles to cover the 40 square foot area.
Calculating the Total Cost of Square Tiles
Now that we know the number of tiles required, we can calculate the total cost of the square tiles.
# Define variables
num_tiles = 400
cost_per_tile = 0.45 # dollars
total_cost = num_tiles * cost_per_tile
print(total_cost)
Running this code, we get:
total_cost = 180.0
So, the total cost of the square tiles would be $180.00.
The Rectangular Tile Option
The rectangular tile is 1 foot by foot, making it a longer and narrower option compared to the square tile. With a cost of $0.35 per tile, Orchid needs to calculate the total number of tiles required to cover the 40 square foot area.
Calculating the Number of Rectangular Tiles Required
To calculate the number of rectangular tiles required, we need to divide the total area of the bathroom floor (40 square feet) by the area of a single rectangular tile (1 foot by foot).
import math
total_area = 40 # square feet
tile_size = 1 # foot
tile_width = 1/3 # foot
num_tiles = total_area / (tile_size * tile_width)
print(num_tiles)
Running this code, we get:
num_tiles = 120
So, Orchid would need 120 rectangular tiles to cover the 40 square foot area.
Calculating the Total Cost of Rectangular Tiles
Now that we know the number of tiles required, we can calculate the total cost of the rectangular tiles.
# Define variables
num_tiles = 120
cost_per_tile = 0.35 # dollars
total_cost = num_tiles * cost_per_tile
print(total_cost)
Running this code, we get:
total_cost = 42.0
So, the total cost of the rectangular tiles would be $42.00.
Comparison of Options
Now that we have calculated the total cost of both options, we can compare them to see which one is more cost-effective.
| Option | Number of Tiles | Total Cost |
|---|---|---|
| Square Tile | 400 | $180.00 |
| Rectangular Tile | 120 | $42.00 |
Based on the calculations, the rectangular tile option is the more cost-effective choice, with a total cost of $42.00 compared to the square tile option's total cost of $180.00.
Conclusion
Introduction
In our previous article, we delved into the mathematical analysis of two custom tile options: square and rectangular. We calculated the number of tiles required and the total cost of each option, determining that the rectangular tile option is the more cost-effective choice. In this article, we will answer some frequently asked questions (FAQs) related to this topic.
Q&A
Q: What is the area of a single square tile?
A: The area of a single square tile is foot by foot, which is equal to 0.25 square feet.
Q: How many square tiles are required to cover a 40 square foot area?
A: To calculate the number of square tiles required, we divide the total area of the bathroom floor (40 square feet) by the area of a single square tile (0.25 square feet). This gives us a total of 160 square tiles.
Q: What is the cost of a single square tile?
A: The cost of a single square tile is $0.45.
Q: What is the total cost of square tiles to cover a 40 square foot area?
A: To calculate the total cost of square tiles, we multiply the number of tiles required (160) by the cost per tile ($0.45). This gives us a total cost of $72.00.
Q: What is the area of a single rectangular tile?
A: The area of a single rectangular tile is 1 foot by foot, which is equal to 0.33 square feet.
Q: How many rectangular tiles are required to cover a 40 square foot area?
A: To calculate the number of rectangular tiles required, we divide the total area of the bathroom floor (40 square feet) by the area of a single rectangular tile (0.33 square feet). This gives us a total of 121 rectangular tiles.
Q: What is the cost of a single rectangular tile?
A: The cost of a single rectangular tile is $0.35.
Q: What is the total cost of rectangular tiles to cover a 40 square foot area?
A: To calculate the total cost of rectangular tiles, we multiply the number of tiles required (121) by the cost per tile ($0.35). This gives us a total cost of $42.35.
Q: Which tile option is more cost-effective?
A: Based on our calculations, the rectangular tile option is the more cost-effective choice, with a total cost of $42.35 compared to the square tile option's total cost of $72.00.
Q: What factors should I consider when choosing a tile option?
A: When choosing a tile option, consider factors such as the area of the bathroom floor, the cost of the tiles, and the number of tiles required. Additionally, consider the aesthetic appeal of the tiles and the ease of installation.
Conclusion
In conclusion, our Q&A article has provided answers to frequently asked questions related to the mathematical analysis of custom tile options. By considering factors such as cost, efficiency, and aesthetic appeal, you can make an informed decision when choosing a tile option for your bathroom flooring.