# Thread: help completing a venn diagram

1. ## help completing a venn diagram

First heres the question:

Three political parties are competing in a local election: the community, equity and green parties. A total of 39 resolutions appear on the ballot and will be voted on in this election. The equity party endorses a total of 15 resolutions. The community party endorses a total of 17 resolutions. The green party endorses a total of 21 resolutions. Five resolutions are endorsed by both equity and community. 8 resolutions are endorsed by both the equity and green. 7 resolutions are endorsed by both the green and community parties. 4 of the resolutions are not endorsed by any of the 3 political parties mentioned above.
a) illustrate this with a venn diagram. Locate appropriate numerical values in all relevant sections of the diagram.
b) How many of the 39 resolutions are endorsed by all 3 political parties.

Now I have no problem actually drawing a venn diagram, what I dont know how to do is figure out the numbers that go in each section. Like how do I figure out how many resolutions are endorsed by all 3? Or how many are endorsed exclusively by each party. Any help greatly appreciated.

2. Originally Posted by ryu991

... I have no problem actually drawing a venn diagram, ...

... how do I figure out how many resolutions are endorsed by all 3? ...

... how many are endorsed exclusively by each party ...
One way to reason it out is to label each of the seven sections with a symbol, use the given information to write a system of seven equations, and solve the system using any method you've learned.

For example, we could label the sections as follows.

A: equity only
B: equity and community only
C: equity and green only
D: all three
E: community only
F: community and green only
G: green only

All seven sections must add up to 35.

A + B + C + D + E + F + G = 35

Equity supports 15 resolutions.

A + B + C + D = 15

Community supports 17 resolutions.

B + D + E + F = 17

Green supports 21 resolutions.

C + D + F + G = 21

We're also told the following.

B + D = 5

C + D = 8

D + F = 7

Do you know how to solve a system of equations?

~ Mark