Answer:

1. The problem asks how many days it will take 10 sewers to finish 200 children's dresses in 8 days, and how many days it will take to finish 300 dresses.

2. The number given is that 5 sewers can finish 200 children's dresses in 8 days.

3. To solve the problem, we need to use the formula:

(number of workers 1 x time 1 x work rate 1) = (number of workers 2 x time 2 x work rate 2)

4. Number sentence:

(5 x 8 x work rate 1) = (10 x time 1 x work rate 2)

(5 x 8 x work rate 1) = (10 x 8 x work rate 2)

(work rate 1) = (16/5) x (work rate 2)

(5 x 8 x 200) = (10 x time 2 x work rate 2)

5. Solution:

From the given information, we know that 5 sewers can finish 200 dresses in 8 days. Therefore, their work rate is:

work rate 1 = (200 dresses) / (5 sewers x 8 days) = 5 dresses per day per sewer

Using the formula above, we can solve for the work rate of 10 sewers:

(work rate 1) = (16/5) x (work rate 2)

(5 dresses per day per sewer) = (16/5) x (work rate 2)

work rate 2 = (5 dresses per day per sewer) x (5/16) x (10) = 15.625 dresses per day per sewer

Finally, we can use the work rate of 15.625 dresses per day per sewer to solve for the number of days it will take to finish 300 dresses:

(5 x 8 x 200) = (10 x time 2 x work rate 2)

(8000) = (10 x time 2 x 15.625)

time 2 = 51.61 days

Therefore, it will take 10 sewers 51.61 days to finish 300 dresses.