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?
How many cars are there not counting the engine and caboose? ** First find the number of cars not counting the engine and caboose: 71 cars - 2 cars = <<71-2=69>>69 cars
How many cars are there? ** 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
Write an equation ** Substituting the second equation into the first, we get p + p/2 + 3 = 69
Combine like terms ** Combining like terms, we get 1.5p + 3 = 69
Subtract 3 ** Subtracting 3 from both sides, we get 1.5p = 66
Divide by 1.5 ** Dividing both sides by 1.5, we get p = 44
#### 44