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Sagot :
Let's analyze the problem step-by-step to determine whose tiles cover the most area per tile.
### Bruce's Tiles
1. Information Given:
- Each tile used by Bruce covers [tex]\(\frac{1}{4}\)[/tex] of a square foot.
2. Calculation:
- The area per tile for Bruce's tiles is [tex]\(\frac{1}{4} = 0.25\)[/tex] square feet per tile.
### Felicia's Tiles
1. Information Given:
- The table lists the number of tiles used by Felicia and the corresponding total area covered:
[tex]\[ \begin{array}{|c|c|} \hline Number of Tiles & Area Covered (sq ft) \\ \hline 6 & 1 \\ \hline 12 & 2 \\ \hline 18 & 3 \\ \hline \end{array} \][/tex]
2. Calculating the Area per Tile:
We will use the data to determine the area per tile. Notice that the relationship between the number of tiles and the total area covered is consistent.
- For 6 tiles, the area covered is 1 square foot.
[tex]\[ \text{Area per tile} = \frac{\text{Total Area}}{\text{Number of Tiles}} = \frac{1 \text{ sq ft}}{6 \text{ tiles}} = \frac{1}{6} \approx 0.1667 \text{ sq ft per tile} \][/tex]
- For 12 tiles, the area covered is 2 square feet.
[tex]\[ \text{Area per tile} = \frac{2 \text{ sq ft}}{12 \text{ tiles}} = \frac{1}{6} \approx 0.1667 \text{ sq ft per tile} \][/tex]
- For 18 tiles, the area covered is 3 square feet.
[tex]\[ \text{Area per tile} = \frac{3 \text{sq ft}}{18 \text{ tiles}} = \frac{1}{6} \approx 0.1667 \text{ sq ft per tile} \][/tex]
Since the area per tile remains consistent across the different data points, we conclude that the area covered by each of Felicia's tiles is:
[tex]\[ \frac{1}{6} \approx 0.1667 \text{ sq ft per tile} \][/tex]
### Comparison
Now we compare the area covered per tile by Bruce and Felicia.
- Bruce's tiles cover [tex]\(0.25\)[/tex] square feet per tile.
- Felicia's tiles cover [tex]\(0.1667\)[/tex] square feet per tile.
### Conclusion
Since [tex]\(0.25\)[/tex] square feet per tile (Bruce's tiles) is greater than [tex]\(0.1667\)[/tex] square feet per tile (Felicia's tiles), Bruce's tiles cover more area per tile. Therefore, Bruce has the tiles that cover the most area per tile.
### Bruce's Tiles
1. Information Given:
- Each tile used by Bruce covers [tex]\(\frac{1}{4}\)[/tex] of a square foot.
2. Calculation:
- The area per tile for Bruce's tiles is [tex]\(\frac{1}{4} = 0.25\)[/tex] square feet per tile.
### Felicia's Tiles
1. Information Given:
- The table lists the number of tiles used by Felicia and the corresponding total area covered:
[tex]\[ \begin{array}{|c|c|} \hline Number of Tiles & Area Covered (sq ft) \\ \hline 6 & 1 \\ \hline 12 & 2 \\ \hline 18 & 3 \\ \hline \end{array} \][/tex]
2. Calculating the Area per Tile:
We will use the data to determine the area per tile. Notice that the relationship between the number of tiles and the total area covered is consistent.
- For 6 tiles, the area covered is 1 square foot.
[tex]\[ \text{Area per tile} = \frac{\text{Total Area}}{\text{Number of Tiles}} = \frac{1 \text{ sq ft}}{6 \text{ tiles}} = \frac{1}{6} \approx 0.1667 \text{ sq ft per tile} \][/tex]
- For 12 tiles, the area covered is 2 square feet.
[tex]\[ \text{Area per tile} = \frac{2 \text{ sq ft}}{12 \text{ tiles}} = \frac{1}{6} \approx 0.1667 \text{ sq ft per tile} \][/tex]
- For 18 tiles, the area covered is 3 square feet.
[tex]\[ \text{Area per tile} = \frac{3 \text{sq ft}}{18 \text{ tiles}} = \frac{1}{6} \approx 0.1667 \text{ sq ft per tile} \][/tex]
Since the area per tile remains consistent across the different data points, we conclude that the area covered by each of Felicia's tiles is:
[tex]\[ \frac{1}{6} \approx 0.1667 \text{ sq ft per tile} \][/tex]
### Comparison
Now we compare the area covered per tile by Bruce and Felicia.
- Bruce's tiles cover [tex]\(0.25\)[/tex] square feet per tile.
- Felicia's tiles cover [tex]\(0.1667\)[/tex] square feet per tile.
### Conclusion
Since [tex]\(0.25\)[/tex] square feet per tile (Bruce's tiles) is greater than [tex]\(0.1667\)[/tex] square feet per tile (Felicia's tiles), Bruce's tiles cover more area per tile. Therefore, Bruce has the tiles that cover the most area per tile.
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