The diagram below represents black and white floor tiles at a size of five by five. If you add to this pattern to make it six by six, how many black tiles would you add to the existing pattern?
I don't know how to solve it, at first I guessed 12 black tiles but it said it was wrong.
We can't see what the pattern is.
Try 11.
5 black tiles
To solve this problem, we need to analyze the existing pattern and determine the ratio of black tiles to white tiles. Let's first count the number of black and white tiles in the provided five by five pattern.
In a five by five pattern, there are 25 total tiles. Now, let's determine the number of black tiles in the pattern. By counting the black tiles in the diagram, we can see that there are 13 black tiles.
Next, let's calculate the ratio of black tiles to total tiles in the existing pattern. To do this, we'll divide the number of black tiles by the total number of tiles: 13 black tiles / 25 total tiles ≈ 0.52.
Now, let's determine how many black tiles would be added to a six by six pattern. In a six by six pattern, there would be a total of 36 tiles. To find the number of black tiles, we'll multiply the total number of tiles by the ratio of black tiles in the existing pattern: 36 total tiles * 0.52 ≈ 18.72.
Since we can't have a fraction of a tile, we'll round our answer to the nearest whole number. Therefore, you would add approximately 19 black tiles to the existing pattern to make it six by six.
It's important to note that this solution assumes the pattern will continue according to the existing ratio. If that's not the case or if the pattern is complex, additional information might be needed to find a precise answer.