Alright, class, let's break down the task step by step to determine whose tiles cover the most area per tile.
### Step 1: Understand Bruce's Tiles
Bruce's tiles each cover [tex]\(\frac{1}{4}\)[/tex] of a square foot in area. This means that:
[tex]\[
\text{Area of one Bruce's tile} = 0.25 \text{ square feet}
\][/tex]
### Step 2: Analyze Felicia's Tiles
We are given a table that shows how much area Felicia's tiles cover for a given number of tiles used.
[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]
For each case in the table, let's calculate the area covered by one of Felicia's tiles.
### Step 3: Calculate Area per Felicia Tile
1. For 6 tiles covering 1 square foot:
[tex]\[
\text{Area per Felicia tile} = \frac{1 \text{ sq ft}}{6} = 0.1667 \text{ sq ft}
\][/tex]
2. For 12 tiles covering 2 square feet:
[tex]\[
\text{Area per Felicia tile} = \frac{2 \text{ sq ft}}{12} = 0.1667 \text{ sq ft}
\][/tex]
3. For 18 tiles covering 3 square feet:
[tex]\[
\text{Area per Felicia tile} = \frac{3 \text{ sq ft}}{18} = 0.1667 \text{ sq ft}
\][/tex]
So, for Felicia's tiles, the area covered by one tile consistently is:
[tex]\[
0.1667 \text{ square feet per tile}
\][/tex]
### Step 4: Compare the Areas Covered per Tile
- Bruce's tile: 0.25 square feet
- Felicia's tile: 0.1667 square feet
### Conclusion
From the calculations, Bruce’s tiles cover [tex]\(\boxed{0.25}\)[/tex] square feet per tile, and Felicia’s tiles cover approximately [tex]\(\boxed{0.1667}\)[/tex] square feet per tile.
Therefore, Bruce's tiles cover more area per tile than Felicia's tiles.
