conversations.from: human
conversations.value: Can you provide an in-depth solution for: A particular train has some passenger cars and a number of cargo cars equal to half the number of passenger cars plus three. If the total number of cars is 71, counting the engine and caboose, how many passenger cars are in the train?Hey there, could you help me solve this math problem: A particular train has some passenger cars and a number of cargo cars equal to half the number of passenger cars plus three. If the total number of cars is 71, counting the engine and caboose, how many passenger cars are in the train?
conversations.from: assistant
conversations.value: First find the number of cars not counting the engine and caboose: 71 cars - 2 cars = 69 cars
  Let p be the number of passenger cars and c be the number of cargo cars. We know that p + c = 69 and c = p/2 + 3
  Substituting the second equation into the first, we get p + p/2 + 3 = 69
  Combining like terms, we get 1.5p + 3 = 69
  Subtracting 3 from both sides, we get 1.5p = 66
  Dividing both sides by 1.5, we get p = 44