Question

the payload of an aircraft is the sum of the weight of the people on board, the weight of their luggage, and the cargo carried by the aircraft. a particular commercial aircraft has a maximum payload of 35,000 kilograms (kg) and cargo weighing 7,000 kg. if (p) represents the number of people on board, and the weight of each person plus his or her luggage is assumed to be 100 kg, which of the following inequalities best represents the situation?
choose 1 answer:
(a) (7,000 + 100pleq35,000)
(b) (7,000 - 100pleq35,000)
(c) (7,000 + 100pgeq35,000)
(d) (100 + 7,000pleq35,000)

Explanation:

Step1: Identify weight components

The weight of cargo is 7000 kg and the weight of each person + luggage is 100 kg. With $P$ people, the total weight of people and their luggage is $100P$ kg.

Step2: Set up inequality based on payload limit

The sum of cargo weight and people - luggage weight must not exceed the maximum payload. So the inequality is $7000 + 100P\leq35000$.

Answer:

A. $7,000 + 100P\leq35,000$