Question

In a class of 50 students.the number of students who offer accounting is twice as the number who offer economics.10 students offer neither of the two subjects and 5 students offer both subjects.Illustrate the information on a Venn diagram.How many students offer accounting?How many students offer economics?How many students offer both subjects?

Answer 1

Within a rectangle, which represents the universal set of 50 students,
draw two intersecting circles, label them A and E
- place 5 in the intersection of the two circles and 10 inside the rectangle, but outside the circles.
- label the A only part as x and the E only part as y
We are told that x + 5 = 2(y + 5)
x = 2y + 5
So change the label of x to 2y+5

From the diagram:
2y+5 + 5 + y + 10 = 50
3y = 30
y = 10
and
x = 20+5 = 25

Now you can re-number all the regions, and therefore all the
questions can be answered