Question 410565
75 owned trucks
112 owned cars
26 owned both a truck and a car
14 owned neither.


you have 75 who owned trucks and 112 who owned cars.


that's a total of 187 who owned a car OR a truck OR both.


out of that 187, 26 owned a car AND a truck.


that means they are being counted twice, so you have to subtract 26 from the total of 187 to get 161 who owned a car OR a truck OR both a car AND a truck.


there are 14 who owned neither a truck or a truck.


since they haven't been counted, you need to add them to the total to get a total of 161 + 14 = 175 people who were interviewed.


here's another way to look at it.


75 owned trucks
112 owned cars
26 owned both a truck and a car
14 owned neither.


separate out people who owned car and truck from people who owned car only and truck only.


you get:


75 - 26 = 49 owned trucks only.
112 - 26 = 86 owned cars only.
26 owned both car and a truck.
14 owned neither.


add 49 + 86 + 26 + 14 to get 175 total


since the 26 who owned cars and trucks were included in the 75 who owned cars and the 112 who owned trucks, you were double counting them.


make the correction by subtracting the ones who owned cars and trucks to get:


75 + 112 + 14 - 26 = 175 total.


that's your answer.


175 people were interviewed.