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

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

D. 25

Step-by-step explanation:

See the file attached.

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]

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.