Of the 80 house in a development, 50 have a two-car garage, 40 have an in-the-ground swimming pool,

Of the 80 house in a development, 50 have a two-car garage, 40 have an in-the-ground swimming pool, and 35 have both a two-car garage and an in-the-ground swimming pool. how many houses in the development have neither a two-car garage nor an in-the-ground swimming pool? a. 10b. 15c. 20d. 25e. 30

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  1. Total number of houses= 80
    number of houses with two garage=50
    number of houses with in-ground swimming pool=40
    number of house with garage and swimming pool=35
    thus number of houses with garage alone=50-35=15
    Number of houses with in-ground swimming pool alone=40-35=5
    Total number of house with atleast a garage of a swimming pool will be:
    (35+15+5)=55

    Number of house that have neither swimming pool nor garage:
    80-55=25 houses

  2. D. 25

    Step-by-step explanation:

    Please find the attachment.

    We have been given that of the 80 house in a development, 50 have a two-car garage, 40 have an in-the-ground swimming pool, and 35 have both a two-car garage and an in-the-ground swimming pool.

    Since 35 have both a two-car garage and an in-the-ground swimming pool, so people, who have only two-car garage would be [tex]50-35=15[/tex].

    The people, who have only in-the-ground swimming pool would be [tex]40-35=5[/tex].

    The number of people, who have two car garage and in-the-ground swimming pool only and have both would be [tex]15+5+35=55[/tex].

    [tex]\text{Houses having neither a two-car garage nor an in-the-ground swimming pool}=80-55[/tex]

    [tex]\text{Houses having neither a two-car garage nor an in-the-ground swimming pool}=25[/tex]

    Therefore, 25 houses in the development have neither a two-car garage nor an in-the-ground swimming pool.

    [tex]Of the 80 house in a development, 50 have a two-car garage, 40 have an in-the-ground swimming pool,[/tex]

  3. Total houses = 80 
    House that have 2 car garage = 50  
    House that an in-the-ground swimming pool = 40
     House that have both 2 car garage and an in-the-ground swimming pool = 35 
     To find: Houses that have neither 2 car garage nor in-the-ground swimming pool. 
     Solution: 
     As total houses = 80, therefore total of all types of houses should be 80.
     Let,
     P = House that have 2 car garage = 50 
     Q = House that an in-the-ground swimming pool = 40
     R = House that have both 2 car garage and an in-the-ground swimming pool= 35
     S = Houses that have neither 2 car garage nor in-the-ground swimming pool
    = ?
      So, P+Q+R+S = 80 
     P+R=50
     Q+R=40 
     R = 35 = house having both 2 car garage and an in-the-ground swimming pool
     putting value of R in above equations, we get
     P = 15 and Q = 5
      P+Q+R+S = 80
     15+5+35+S = 80 
     S = 25 
      Number of houses that have neither 2 car garage nor in-the-ground swimming pool are 25.

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