https://file.aiquickdraw.com/mathbot/file/17290495211885vr6plaa.jpg

Let's solve the problem using the Venn diagram in the image.

We are given a survey of 449 students about drinking tea and coffee, and a Venn diagram displaying the following information:
- 97 students drink only tea.
- 199 students drink only coffee.
- 66 students drink both tea and coffee.
- 87 students neither drink tea nor coffee.

### Questions:

1. **(a) How many of the students drink coffee?**

To find the total number of students who drink coffee, we need to add those who drink only coffee and those who drink both coffee and tea:
- Drink only coffee: 199
- Drink both: 66

So, the total number of students who drink coffee is:
\[
199 + 66 = 265 \text{ students}
\]

2. **(b) How many of the students drink tea or coffee (or both)?**

This is asking for the total number of students who drink either tea, coffee, or both. This includes:
- Only tea: 97
- Only coffee: 199
- Both tea and coffee: 66

Thus, the total number of students who drink tea or coffee is:
\[
97 + 199 + 66 = 362 \text{ students}
\]

3. **(c) How many of the students do not drink both tea and coffee?**

From the Venn diagram, we are told that 87 students drink neither tea nor coffee. This is the answer for this part.

Thus, the answers are:
- (a) 265 students
- (b) 362 students
- (c) 87 students

Do you need further details on these calculations or have any additional questions? 

### 5 Related Questions:
1. How would the results change if the number of students drinking both tea and coffee increased by 10?
2. What percentage of the surveyed students drink only tea?
3. If 10 more students started drinking only coffee, how many would drink coffee in total?
4. How would the number of students drinking neither tea nor coffee affect the total survey size?
5. Can you calculate the probability that a randomly selected student drinks both tea and coffee?

### Tip:
When interpreting Venn diagrams, always remember to add the overlapping and non-overlapping regions to get totals for combined groups.

A college food court surveyed 449 students to see how many drink tea and how many drink coffee. The Venn diagram shows the results. (Each number gives the number of students who fall into that Venn diagram category). How many students drink coffee, tea or coffee (or both), and how many do not drink both tea and coffee?

Solve a Venn diagram problem that surveys 449 students about their tea and coffee consumption habits. Learn how many students drink coffee, tea, or both, and how many do not drink either. This problem uses set theory and basic arithmetic concepts, suitable for Grades 8-10.

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