Final answer:
A total of 9 cable cars will be filled with the 51 people in line and 3 more people are needed to fill the next cable car.
Step-by-step explanation:
Part A: To determine how many cable cars will be filled, we need to divide the total number of people in line by the capacity of each cable car. 51 people / 6 riders per cable car = 8.5 cable cars. However, since we cannot have fractional cable cars, we round up to the nearest whole number. Therefore, the people in line will fill 9 cable cars.
Part B: To determine how many more people are needed to fill the next cable car, we need to find the remainder after dividing the total number of people by the capacity of each cable car. 51 people % 6 riders per cable car = 3 remaining people. Therefore, 3 more people are needed to fill the next cable car.