To determine whose tiles cover the most area per tile, we'll first analyze and extract the necessary information about the tiles used by both Bruce and Felicia.
### Bruce's Tiles
Bruce uses tiles that each cover [tex]\(\frac{1}{4}\)[/tex] of a square foot.
### Felicia's Tiles
Felicia's tile data is provided in a table format which shows the number of tiles and the corresponding total area covered:
[tex]\[
\begin{array}{|c|c|}
\hline
\text{Number of Tiles} & \text{Area Covered (sq ft)} \\
\hline
6 & 1 \\
\hline
12 & 2 \\
\hline
18 & 3 \\
\hline
\end{array}
\][/tex]
### Calculate Area Covered Per Tile for Felicia
To find out how much area each of Felicia's tiles covers, we use the data from the table and perform the following calculations:
1. For 6 tiles:
[tex]\[
\text{Area per tile} = \frac{1 \text{ sq ft}}{6 \text{ tiles}} = \frac{1}{6} \text{ sq ft/tile}
\][/tex]
2. For 12 tiles:
[tex]\[
\text{Area per tile} = \frac{2 \text{ sq ft}}{12 \text{ tiles}} = \frac{2}{12} = \frac{1}{6} \text{ sq ft/tile}
\][/tex]
3. For 18 tiles:
[tex]\[
\text{Area per tile} = \frac{3 \text{ sq ft}}{18 \text{ tiles}} = \frac{3}{18} = \frac{1}{6} \text{ sq ft/tile}
\][/tex]
We see that each calculation gives [tex]\(\frac{1}{6}\)[/tex] square feet per tile. This indicates uniformity in the tile size used by Felicia.
### Conclusion
Now we compare the area per tile for both Bruce and Felicia:
- Bruce's tiles: Each covers [tex]\(\frac{1}{4}\)[/tex] square feet.
- Felicia's tiles: Each covers [tex]\(\frac{1}{6}\)[/tex] square feet.
To determine who has the tiles that cover the most area, we compare the fractions:
[tex]\[
\frac{1}{4} = 0.25 \text{ sq ft/tile}
\][/tex]
[tex]\[
\frac{1}{6} \approx 0.167 \text{ sq ft/tile}
\][/tex]
Since [tex]\(0.25 \text{ sq ft/tile} > 0.167 \text{ sq ft/tile}\)[/tex], Bruce's tiles cover more area per tile than Felicia's tiles.
