https://file.aiquickdraw.com/mathbot/file/1729637672245wg7h4yph.jpg

Let's break down the problem using the information from the Venn diagram.

We are given a total of 410 students, and the diagram divides these students based on whether they drink soda, coffee, or both.

### Venn Diagram Numbers:
- 33 students drink only soda.
- 113 students drink both soda and coffee.
- 22 students drink only coffee.
- 242 students do not drink either soda or coffee.

### Questions:
#### (a) How many of the students do not drink soda?
Students who **do not drink soda** are those outside the "Drink soda" circle. This includes:
- 22 students who drink only coffee.
- 242 students who drink neither soda nor coffee.

So, the total number of students who do not drink soda is:
\[
22 + 242 = 264 \text{ students}.
\]

#### (b) How many of the students drink soda or coffee (or both)?
Students who drink **soda or coffee (or both)** are those in either or both of the circles. This includes:
- 33 students who drink only soda.
- 113 students who drink both soda and coffee.
- 22 students who drink only coffee.

So, the total number of students who drink soda or coffee is:
\[
33 + 113 + 22 = 168 \text{ students}.
\]

#### (c) How many of the students drink soda but do not drink coffee?
Students who drink **only soda** are given directly in the diagram:
\[
33 \text{ students}.
\]

### Summary of Answers:
- (a) 264 students do not drink soda.
- (b) 168 students drink soda or coffee (or both).
- (c) 33 students drink soda but do not drink coffee.

Would you like more details or explanations on any part? 

Here are some related questions for further practice:
1. How many students drink only coffee?
2. How many students do not drink coffee?
3. What percentage of students drink both soda and coffee?
4. How many students drink neither soda nor coffee?
5. How many more students drink coffee compared to soda?

**Tip:** Venn diagrams are useful for visualizing sets and their relationships, especially when solving problems related to inclusion and exclusion.

A college food court surveyed 410 students to see how many drink soda and how many drink coffee. The Venn diagram shows the results, and the following questions need to be answered:
(a) How many of the students do not drink soda?
(b) How many of the students drink soda or coffee (or both)?
(c) How many of the students drink soda but do not drink coffee?

Solve a Venn diagram problem from a college survey of 410 students. Learn how to determine how many students drink soda, coffee, both, or neither. Understand key set theory concepts, including the principle of inclusion and exclusion, with a clear step-by-step explanation. Suitable for middle school students in Grades 6-8.

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