The Greens are moving. Their real estate agent located 81 houses listed for sale in their price range. Of those houses listed for sale, 51 had a finished basement.

56 had a three-car garage.

37 had a finished basement and a three-car garage.

Complete parts a) through c).

a) How many had a finished basement but not a three-car garage?

b) How many had a three-car garage but not a finished basement?

c) How many had either a finished basement or a three-car garage?

We know that:

There is a total of 81 houses:

51 had a finished basement.

56 had a three-car garage.

37 had a finished basement and a three-car garage.

a)  How many had a finished basement but not a three-car garage?

51 had a finished basement, and 37 have a finished basement and the garage, then:

51 - 37 = 14 hoses have only the basement.

b) How many had a three-car garage but not a finished basement?

Same reasoning as above:

56 - 37 = 19 houses only have the garage.

c) How many had either a finished basement or a three-car garage?

Now we only count the ones that have one finished thing, in this case, we already found the number of houses that have only the garage or only the basement, then the number of houses that either had a finished basement or a finished garage is:

19 + 18 = 37 houses.

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