Answer to Question #177922 in Math for Owusu Stephen

Question

In class of 35 student, each student studies history and geography.twice as many study history are studying geography 1/2 as many study both subject are studying only history.illustrate the information on Venn diagram.both subject.geography.only history only one subject

Answer 1

Let set H be the set of students studying history, and let set G be the group of students studying geography.

n(H) = 2x , n(G) = x

n(H∩G) = 0.5×(n(H) - n(H∩G)) = x - 0.5n(H∩G))

n(H∩G) = 2/3x.

2x + x - 2/3x = 35,

x = 35×3/7 = 15,

So, 30 students study history, 15 students study geography, 10 students study both subjects, 20 students study only history and 5 students study only geography.

The Venn diagram will look like 2 circles, first circle H has area of 30, second circle G has area of 15, and the intersection of them has area of 10.