Question 1198758: The members of a College staff club were asked to indicate the brand of beer they drink. 5 members drank stars and Trophy beers, 7 members drank star and club beers, 6 members drank starbeer only, 11 drank Trophy beer only while 5 drank club only. Three members drank all the three brands. assuming that each member drank at least one brand of beer, Find
i, the number of members that drank star beer
ii, the number of members that drank Trophy beer
iii, the number of members that drank club beer
iv, the total number of members in the club
Found 2 solutions by math_tutor2020, MathTherapy:
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
Here's the venn diagram with 8 distinct regions
The region labels are:
S = people who drank star beer only
T = people who drank trophy beer only
C = people who drank club beer only
ST = people who drank star and trophy, but not club
TC = people who drank trophy and club, but not star
SC = people who drank star and club, but not trophy
STC = people who drank all three brands
N = people who drank none of the three brands mentioned
Given Facts:
| Number | Fact | | 1 | 5 members drank stars and Trophy beers | | 2 | 7 members drank star and club beers | | 3 | 6 members drank starbeer only | | 4 | 11 drank Trophy beer only | | 5 | 5 drank club only | | 6 | 3 members drank all the three brands | | 7 | Each member drank at least one brand of beer |
Fact 6 indicates the value "3" goes in region STC.
Facts 1 and 6 will lead to 5-3 = 2 members who drank stars and trophy, but not club beer. Write "2" in region ST
Facts 2 and 6 will lead to 7-3 = 4 members who drank star and club, but not trophy beer. Write "4" in region SC
Fact 3 indicates we'll write "6" in region S.
Fact 4 indicates we'll write "11" in region T.
Fact 5 indicates we'll write "5" in region C.
Fact 7 means we have "0" in region N, because each person drank at least one type.
This is what we have so far
Your teacher doesn't give enough info to determine what value goes in region TC.
I would ask your teacher for clarification about this.
------------------------------------------------------
i, the number of members that drank star beer
We add up the values inside the circle labeled "Star"
6+2+4+3 = 15
Answer: 15 people drank star beer
------------------------------------------------------
ii, the number of members that drank Trophy beer
Like I mentioned earlier, we don't know what value goes in region TC.
We unfortunately do not have enough information to determine how many people drank trophy beer.
Similar situations apply to the remaining questions as well.
Answer by MathTherapy(10552)  (Show Source):
You can put this solution on YOUR website! The members of a College staff club were asked to indicate the brand of beer they drink. 5 members drank stars and Trophy beers, 7 members drank star and club beers, 6 members drank starbeer only, 11 drank Trophy beer only while 5 drank club only. Three members drank all the three brands. assuming that each member drank at least one brand of beer, Find
i, the number of members that drank star beer
ii, the number of members that drank Trophy beer
iii, the number of members that drank club beer
iv, the total number of members in the club
 .
The answers to your questions, i) - iv) are derived from the above Venn Diagram, and are based on the following:
1) Zero (0) members drink Trophy and Club beers, only.
2) All members of the club are beer drinkers.
So, i, the number of members that drank star beer: 6 + 2 + 3 + 4 = 15
ii, the number of members that drank Trophy beer: 11 + 2 + 3 + 0 = 16
iii, the number of members that drank club beer: 5 + 4 + 3 + 0 = 12
iv, the total number of members in the club: 11 + 2 + 3 + 0 + 6 + 4 + 5 = 31
|
|
|
