Beverage survey A survey of 150 students asked which of the following three beverages they liked: sodas, coffee, or bottled water. The results are given in the

Question

Beverage survey A survey of 150 students asked which of the following three beverages they liked: sodas, coffee, or bottled water. The results are given in the table below.

Sodas Only- 28

Coffee Only- 17

Water- 51Sodas and water- 34

Coffee and water- 27

Sodas and coffee but not water- 9

Coffee and water, not sodas- 6

All three- 21

 

 

Use S for soda, W for water, and C for coffee, and make a Venn diagram for drinks. The completed diagram should show the number in each region.

Answer the following questions:

(Give all of your answers as whole numbers.)


How many students like coffee only?
- I know that this is 17

How many students liked water but not coffee?
- I know that this is 24

How many students liked none of the three beverages?
-

How many students liked coffee and water?
- I know this is 27

How many students liked exactly two of the three beverages?
-

How many students liked exactly one of the three beverages?
- I know this is 64

Answer 1

Here is another rather crude Venn Diagram  (with imaginary circles):

 

   150 total

 

         45 others
 
            S                                               W
                28                   13               11
 
                                     21
 
                         9                     6
 
                                      17
                                       C

 

Questions:

 

How many students like coffee only?
- I know that this is 17    yep

How many students liked water but not coffee?
- I know that this is 24     yep

How many students liked none of the three beverages?
- 150 - 28 - 13 - 11 - 21 - 9 - 6 - 17  =  45

How many students liked coffee and water?
- I know this is 27       yep

How many students liked exactly two of the three beverages?
-     13 + 9 + 6 = 28

How many students liked exactly one of the three beverages?
- I know this is 64    Hmmm ... 28 + 11 + 17  = 56

Answer 2

 

How many students liked none of the three beverages? 45 students. 150-28-17-21-9-6-13-11=45

 

The total number of students is 150. Subtract 28 and 17 from 150 since these students only like soda or coffee. 21 students like all 3 beverages. We are given 9 students like soda and coffee and 6 like coffee and water but we must find how many like soda and water but not coffee. They say 34 students like soda and water but 21 are already accounted for so 34-21=13 students. We also know 51 students like water. To solve for how many students only like water, solve 51-13-21-6=11. Finally, we take all these numbers and subtract them from 150 to find how many students don't like any of the 3 beverages.

 

How many students liked exactly two of the three beverages? 28 students. 9+13+6=28

 

We have to add the students who like coffee and soda but not water, coffee and water but not soda, and soda and water but not coffee. We want the numbers within the interlocking circles except for 21 since these students like all 3 beverages and not just 2.