Answer:
A total of 160 adult plates and 90 children's plates were sold.
Explanation:
Given that the Buck Creek Fire Department served 250 dinners, and that a child's plate costs $ 5.50 while an adult's plate costs $ 9.00, having collected a total of $ 1935, to determine how many dishes of each type were served, the following calculation must be performed: 
9 - 5.5 = 3.5 
250 x 5.5 = 1,375 
1,935 - 1,375 = 560 
560 / 3.5 = 160 
160 x 9 = 1,440 
90 x 5.5 = 495 
1,440 + 495 = X 
1,935 = X 
Thus, a total of 160 adult plates and 90 children's plates were sold.