Question

Without any passengers, an aeroplane has a mass of 4200 kg. The plane has capacity to carry 120 passengers, and when there are 40 passengers on the plane, the total mass of the plane and passenger is 7480 kg.

a) calculate the mean mass of passenger
b) Hence, write an expression for un that gives the total mass of the plane and passengers when there are n passengers on board
c) state the values of n for which your model is valid

Answer 1

The mean mass of a passenger is 82 kg. The expression for the total mass with n passengers is un = (n × 82 kg) + 4200 kg. The model is valid for values of n between 0 and 120.

Step-by-step explanation:

To calculate the mean mass of a passenger, we need to find the total mass of the passengers on the plane and divide it by the number of passengers. The total mass of the plane and 40 passengers is 7480 kg. So, the mass of the 40 passengers is the difference between the total mass and the mass of the plane (7480 kg - 4200 kg = 3280 kg). Therefore, the mean mass of a passenger is 3280 kg divided by 40, which is 82 kg.

To write an expression for un that gives the total mass of the plane and passengers when there are n passengers on board, we can use the fact that the difference between the total mass with n passengers and the mass of the plane is equal to the mass of the n passengers. So, un = (n × mean mass of passenger) + mass of the plane. In this case, un = (n × 82 kg) + 4200 kg.

The model is valid for values of n greater than or equal to 0 and less than or equal to 120, since the plane has a capacity to carry 120 passengers.