Question

Of the 80 houses 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?

Answer 1

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 
 Answer: Number of houses that have neither 2 car garage nor in-the-ground swimming pool are 25.