Let's go through the problem step by step to determine which type of tile Orchid should choose to minimize costs.
Step 1: Calculate the area of each type of tile
- Square tile:
The side length of the square tile is [tex]\( \frac{1}{2} \)[/tex] foot.
The area of one square tile [tex]\( = (\frac{1}{2}) \times (\frac{1}{2}) = \frac{1}{4} \)[/tex] square feet.
- Rectangular tile:
The dimensions of the rectangular tile are 2 feet by [tex]\( \frac{1}{4} \)[/tex] foot.
The area of one rectangular tile [tex]\( = 2 \times \frac{1}{4} = \frac{1}{2} \)[/tex] square feet.
Step 2: Calculate the number of tiles needed to cover the bathroom floor
- Square tiles:
Total area of the bathroom floor [tex]\( = 40 \)[/tex] square feet.
Number of square tiles required [tex]\( = \frac{40}{\frac{1}{4}} = 160 \)[/tex] tiles.
- Rectangular tiles:
Number of rectangular tiles required [tex]\( = \frac{40}{\frac{1}{2}} = 80 \)[/tex] tiles.
Step 3: Calculate the total cost for each type of tile
- Square tiles:
Cost of one square tile [tex]\( = \$90.45 \)[/tex].
Total cost for square tiles [tex]\( = 160 \times 90.45 = \$14,472 \)[/tex].
- Rectangular tiles:
Cost of one rectangular tile [tex]\( = \$0.80 \)[/tex].
Total cost for rectangular tiles [tex]\( = 80 \times 0.80 = \$64 \)[/tex].
Step 4: Calculate the difference in cost
The difference in cost [tex]\( = \$14,472 - \$64 = \$14,408 \)[/tex].
Step 5: Determine which tile to choose
Since the total cost for the rectangular tiles (\[tex]$64) is significantly less than the total cost for the square tiles (\$[/tex]14,472), Orchid should choose the rectangular tiles to minimize costs.
Based on this analysis:
- Conclusion: She should choose the rectangular tiles because the total cost will be \$14,408 less.
