Sure, let's analyze Marco's arrangement of tiles and determine the expression he might have written.
Given the tile arrangement:
[tex]\[
\begin{tabular}{|l|l|l|}
\hline
a & a & b \\
\hline
a & a & b \\
\hline
\end{tabular}
\][/tex]
First, let's count the number of each type of tile.
1. Counting the `a` tiles:
- Observe that each row has 2 `a` tiles.
- Since there are 2 rows, the total number of `a` tiles is:
[tex]\[
2 \text{ (per row)} \times 2 \text{ (rows)} = 4 \text{ tiles}
\][/tex]
2. Counting the `b` tiles:
- Observe that each row has 1 `b` tile.
- Since there are 2 rows, the total number of `b` tiles is:
[tex]\[
1 \text{ (per row)} \times 2 \text{ (rows)} = 2 \text{ tiles}
\][/tex]
Now that we know the counts, we can write the corresponding expression that Marco might have written based on his arrangement:
[tex]\[
4a + 2b
\][/tex]
So, the expression Marco might have written is:
[tex]\[
4a + 2b
\][/tex]
This expression accurately represents the distribution and quantity of the tiles in Marco's arrangement.
