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.

Question

(1 point)

Answer 1

The pattern of tiles is "Blue, White, Black," which consists of 3 tiles.

To determine how many complete cycles of the pattern are in 85 tiles, we divide 85 by 3:

$$85÷3=28\text{(whole number)}$$ with a remainder of 1, which means there are 28 complete cycles of the pattern and an extra 1 tile beyond that.

In each complete cycle of 3 tiles, there is 1 black tile. So, the number of black tiles from the complete cycles is:

$$28\text{ (complete cycles)}\times 1\text{ (black tile per cycle)}=28\text{ black tiles}$$

Now we consider the extra tile. The first tile in the repeating pattern is blue. So the additional tile does not add to the count of black tiles.

Thus, the total number of black tiles used is:

$$\text{Total black tiles}=28$$

Therefore, the final answer is:

28