Question 410565: A car dealership interviewed every driver who came onto their lot on Tuesday. This produced the following results: there were 75 people who owned trucks and 112 people who owned cars. If 26 people owned both a truck and a car and 14 people owned neither, how many people were interviewed?
can some one help me
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 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.
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