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.