SOLUTION: In a town, 80% of the houses have water and 34% of the houses have no electricity. A quarter of the houses with water have no electricity. What percetage of the houses have neither
Question 1135339: In a town, 80% of the houses have water and 34% of the houses have no electricity. A quarter of the houses with water have no electricity. What percetage of the houses have neither water nor elecricity? Found 2 solutions by Boreal, ikleyn:Answer by Boreal(15235) (Show Source):
You can put this solution on YOUR website! This is what is given
Water Y-----N- Tot
Elec Y *************66
Elec N***************34
Tot *******80*****20**100
a quarter of the houses with water have no electricity, so that is 20
Water Y-----N- Tot
Elec Y **************66
Elec N******20********34
Tot ********80****20***100
Fill in the rest
Water Y-----N- Tot
Elec Y -----60 --6-- 66
Elec N------20----14---34
Tot ------80----20 100
14% have neither water nor electricity
Let H be the number of houses in the town.
In this problem, we are given
a) the set of the houses in the town that HAVE WATER (80% of all houses of the town). Let's call this set W.
b) the set of the houses in the town that HAVE NO ELECTRICITY (34% of all houses of the town). Let's call this set NE.
c) also, we know that "A quarter of the houses with water have no electricity".
In other words, 0.25*(0.8*H) = 0.2H houses belong to the intersection (W n NE).
The question is how many houses is in the set NE \ (W n NE). (<<<---=== the difference of the set NE and its subset (W n NE) ).
Obviously, the answer is 0.34H - 0.2H = 0.14H.
Thus the answer to the problem's question is 14%.
