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The payload of an aircraft is the sum of the weight of the people on board, 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 7,000kg. If P represents the number of people on board, and the weight of each person plus his or her luggage is assumed to be 100kg, which of the following inequalities best represents the situation? Choose 1 answer: (A) 7,000+100 P <= 35,000 (B) 7,000-100 P <= 35,000 (C) 7,000+100 P >= 35,000 (D) 100+7,000 P <= 35,000

The payload of an aircraft is the sum of the weight of the people on board, their luggage, and the cargo carried by the aircraft. A particular commercial aircraft has a maximum payload of 3535,000000 kilograms (kg) (\mathrm{kg}) and cargo weighing 7,000 kg 7,000 \mathrm{~kg} . If P 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 100 \mathrm{~kg} , which of the following inequalities best represents the situation?\newlineChoose 11 answer:\newline(A) 7,000+100P≤35,000 7,000+100 P \leq 35,000 \newline(B) 7,000−100P≤35,000 7,000-100 P \leq 35,000 \newline(C) 7,000+100P≥35,000 7,000+100 P \geq 35,000 \newline(D) 100+7,000P≤35,000 100+7,000 P \leq 35,000

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Q. The payload of an aircraft is the sum of the weight of the people on board, their luggage, and the cargo carried by the aircraft. A particular commercial aircraft has a maximum payload of 3535,000000 kilograms (kg) (\mathrm{kg}) and cargo weighing 7,000 kg 7,000 \mathrm{~kg} . If P 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 100 \mathrm{~kg} , which of the following inequalities best represents the situation?\newlineChoose 11 answer:\newline(A) 7,000+100P≤35,000 7,000+100 P \leq 35,000 \newline(B) 7,000−100P≤35,000 7,000-100 P \leq 35,000 \newline(C) 7,000+100P≥35,000 7,000+100 P \geq 35,000 \newline(D) 100+7,000P≤35,000 100+7,000 P \leq 35,000
  1. Identify maximum payload and cargo weight: Identify the maximum payload of the aircraft and the weight of the cargo.\newlineThe maximum payload is given as 35,000 kg35,000\,\text{kg}, and the cargo weighs 7,000 kg7,000\,\text{kg}.
  2. Determine remaining payload capacity: Determine the remaining payload capacity for people and their luggage.\newlineSubtract the weight of the cargo from the maximum payload to find the remaining capacity.\newline35,000 kg35,000\,\text{kg} (maximum payload) −- 7,000 kg7,000\,\text{kg} (cargo weight) == 28,000 kg28,000\,\text{kg}
  3. Represent weight of people and luggage: Represent the weight of the people and their luggage using the variable PP. Each person with their luggage is assumed to weigh 100 kg100\,\text{kg}, so the total weight of PP people is 100 kg×P100\,\text{kg} \times P, or 100P100P.
  4. Formulate the inequality: Formulate the inequality that represents the situation.\newlineThe sum of the cargo weight and the weight of the people must be less than or equal to the maximum payload.\newlineTherefore, the inequality is 7,000 kg7,000\,\text{kg} (cargo weight) + 100 kg×P100\,\text{kg} \times P (weight of people) ≤35,000 kg\leq 35,000\,\text{kg} (maximum payload).
  5. Choose correct inequality: Choose the correct inequality from the given options.\newlineThe correct inequality that represents the situation is 7,000+100P≤35,0007,000 + 100P \leq 35,000, which corresponds to option (A).

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