Sam is tiling a floor. He will use the same repeating pattern for the entire floor. The rule is "Blue Tile, White Tile, Black Tile." If he uses 85 tiles, how many will be black? Enter your answer in the box.

Answer 1

To determine how many black tiles Sam uses, we first need to recognize the repeating pattern: Blue Tile, White Tile, Black Tile. This pattern consists of 3 tiles.

Next, we need to find how many complete sets of this pattern will fit within the 85 tiles. We can do this by dividing the total number of tiles by the number of tiles in the pattern:

\[ \text{Number of complete sets} = \frac{85}{3} = 28 \text{ sets} \text{ with a remainder of } 1. \]

This means there are 28 complete sets of the pattern, and the remainder (1) indicates that there is one additional tile after the complete sets.

Each complete set of the pattern contains 1 black tile. Therefore, the total number of black tiles from the 28 complete sets is:

\[ \text{Black tiles from complete sets} = 28 \times 1 = 28. \]

Now, we need to account for the additional tile. Since the repeating pattern starts with a Blue tile, the additional tile will be a Blue tile as well.

Thus, the total number of black tiles Sam will use is:

\[ \text{Total black tiles} = 28. \]

Finally, the answer is:

\[ \boxed{28} \]