Venn Diagram Worksheets and Templates - Free Printable

Problem Analysis:

The problem involves a Venn diagram with two sets: Juice and Soda. We are given the following information:
- Total visitors: 200
- Visitors who ordered juice only: 87
- Visitors who ordered soda only: 53
- Visitors who ordered both juice and soda: 5
- The rest did not order any drink.

We need to fill in the Venn diagram and answer several questions based on the given data.

Step-by-Step Solution:

#### 1. Fill in the Venn Diagram:
- Juice only: 87
- Soda only: 53
- Both Juice and Soda: 5

To find the number of visitors who did not order any drink, we use the total number of visitors (200) and subtract those who ordered either juice, soda, or both:
\[
\text{Total visitors} = \text{Juice only} + \text{Soda only} + \text{Both} + \text{Neither}
\]
\[
200 = 87 + 53 + 5 + \text{Neither}
\]
\[
200 = 145 + \text{Neither}
\]
\[
\text{Neither} = 200 - 145 = 55
\]

So, the Venn diagram is filled as follows:
- Juice only: 87
- Soda only: 53
- Both Juice and Soda: 5
- Neither: 55

#### 2. Answer the Questions:

##### Question 1: How many visitors do not like either juice or soda?
This corresponds to the "Neither" section of the Venn diagram.
\[
\boxed{55}
\]

##### Question 2: How many visitors like juice?
This includes visitors who ordered juice only and those who ordered both juice and soda.
\[
\text{Like Juice} = \text{Juice only} + \text{Both}
\]
\[
\text{Like Juice} = 87 + 5 = 92
\]
\[
\boxed{92}
\]

##### Question 3: How many visitors do not like soda?
This includes visitors who ordered juice only and those who did not order any drink.
\[
\text{Do not like Soda} = \text{Juice only} + \text{Neither}
\]
\[
\text{Do not like Soda} = 87 + 55 = 142
\]
\[
\boxed{142}
\]

##### Question 4: How many visitors only like soda?
This corresponds to the "Soda only" section of the Venn diagram.
\[
\boxed{53}
\]

##### Question 5: How many visitors do not like both juice and soda?
This corresponds to the "Neither" section of the Venn diagram.
\[
\boxed{55}
\]

##### Question 6: How many visitors like soda?
This includes visitors who ordered soda only and those who ordered both juice and soda.
\[
\text{Like Soda} = \text{Soda only} + \text{Both}
\]
\[
\text{Like Soda} = 53 + 5 = 58
\]
\[
\boxed{58}
\]

##### Question 7: How many visitors like juice or soda?
This includes visitors who ordered juice only, soda only, and both juice and soda.
\[
\text{Like Juice or Soda} = \text{Juice only} + \text{Soda only} + \text{Both}
\]
\[
\text{Like Juice or Soda} = 87 + 53 + 5 = 145
\]
\[
\boxed{145}
\]

##### Question 8: How many visitors do not like juice?
This includes visitors who ordered soda only and those who did not order any drink.
\[
\text{Do not like Juice} = \text{Soda only} + \text{Neither}
\]
\[
\text{Do not like Juice} = 53 + 55 = 108
\]
\[
\boxed{108}
\]

Final Answers:

1. \( \boxed{55} \)
2. \( \boxed{92} \)
3. \( \boxed{142} \)
4. \( \boxed{53} \)
5. \( \boxed{55} \)
6. \( \boxed{58} \)
7. \( \boxed{145} \)
8. \( \boxed{108} \)

Explanation:

The solution uses the principles of set theory and Venn diagrams to organize and analyze the given data. By breaking down the problem into sections (juice only, soda only, both, neither), we can systematically answer each question. The key is to ensure that all visitors are accounted for and that overlaps are correctly handled.