Respuesta :
When Arthur finished 100 snowflakes, Brian had 20 left, meaning Brian had made 80 snowflakes by the time Arthur made 100.
When Brian finished his 100 snowflakes, Carl had 20 left, meaning Carl had made 80 snowflakes by the time Brian made 100.
The key here is to determine the relationship between their rates of making snowflakes. Since Brian made 80 snowflakes in the same time it took Arthur to make 100, Brian's rate compared to Arthur's is 80:100, or simplified, 4:5. This means for every 4 snowflakes Brian makes, Arthur makes 5.
Similarly, Carl made 80 snowflakes in the time it took Brian to make 100, so Carl's rate compared to Brian's is also 4:5. This means for every 4 snowflakes Carl makes, Brian makes 5.
Now, we need to figure out how many snowflakes Carl had left when Arthur finished his 100th snowflake. Since Brian's rate compared to Arthur's is 4:5, and Carl's rate compared to Brian's is also 4:5, we can establish the relative rate of Carl to Arthur by multiplying these ratios together:
The combined ratio of Carl's work to Arthur's, based on their work compared to Brian's, is (4/5) * (4/5) = 16/25.
So, for every 25 snowflakes Arthur makes, Carl makes 16. When Arthur finished 100 snowflakes (which is 4 times 25), Carl would have made 4 times 16 snowflakes, because 100 snowflakes completed by Arthur corresponds to 4 * 25 in our ratio.
Therefore, Carl would have made 64 snowflakes by the time Arthur finished 100.
To find out how many snowflakes Carl had left when Arthur finished, we subtract Carl's completed snowflakes from the total:
100 total snowflakes - 64 snowflakes made by Carl = 36 snowflakes left for Carl.
Thus, when Arthur finished his 100th snowflake, Carl had 36 snowflakes left to make
