Question

Of the 75 houses in a certain community, 48 have a patio. How many of the houses in the community have a swimming pool? (1) 38 of the houses in the community have a patio but do not have a swimming pool. (2) The number of houses in the community that have a patio and a swimming pool is equal to the number of houses in the community that have neither a swimming pool nor a patio.

Answer 1

(2) The number of houses in the community that have a patio and a swimming pool is equal to the number of houses in the community that have neither a swimming pool nor a patio.

Step-by-step explanation:

P= #Just houses with patio.

Q= #Just house with lake.

R= #Patio & Pool Rooms.

S= #Without Patio Houses & No Pool.

What is Q+R, given P+Q+R+S=75 & P+R=48? (1) Resolving the first two equations Q+S+48=75 Q+S=27(2) Let us now look at the statements Statement 1 P=38, which are unnecessary and insufficient.

Claim 2 R= S Substitute Q+S in (1)?

We know form (2) that Q+S= 27 is adequate for that.

Answer 2

27 houses have swimming pool

Step-by-step explanation:

Then the Question states that the number of houses with a patio and swimming pool are the same as the ones who don't and the question also states that 38 of the 48 houses only have patios then 10 houses have swimming pools and a patio. So it can be concluded that 10 houses do not have swimming pool and patio. So we can safely deduce that 75 minus 38(houses with only patio) equals 37 and 37 minus 10(houses without patio and swimming pool) equals 27.