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The problem on your screen reads:

> In a group of 20 people, 13 people like tea, 12 people like coffee, and 3 people like neither tea nor coffee. How many people like tea but not coffee?

Let's break this down step by step:

1. **Total group size** = 20 people
2. **People who like neither tea nor coffee** = 3 people
3. Therefore, the number of people who like either tea or coffee (or both) = \( 20 - 3 = 17 \) people.
4. **People who like tea** = 13 people
5. **People who like coffee** = 12 people

Let \( x \) represent the number of people who like both tea and coffee. 

Now, the equation for those who like either tea or coffee can be written as:
\[
\text{People who like tea} + \text{People who like coffee} - \text{People who like both} = 17
\]
Substituting the values:
\[
13 + 12 - x = 17
\]
Solving for \( x \):
\[
25 - x = 17 \implies x = 8
\]

So, 8 people like both tea and coffee.

Now, to find how many people like tea but **not** coffee:
\[
\text{People who like only tea} = \text{People who like tea} - \text{People who like both tea and coffee} = 13 - 8 = 5
\]

Thus, **5 people like tea but not coffee**.

Would you like more details on this solution or further clarifications?

Here are 5 related questions to expand your understanding:
1. How many people like only coffee but not tea?
2. What is the total number of people who like coffee (including both coffee-only and tea+coffee)?
3. How would the answer change if 4 people liked neither tea nor coffee?
4. Can this problem be solved using Venn diagrams? If so, how?
5. How many people like either tea or coffee but not both?

**Tip:** Problems like this often benefit from drawing a Venn diagram to visualize the overlaps between groups.

In a group of 20 people, 13 people like tea, 12 people like coffee and 3 people like neither tea nor coffee. How many people like tea but not coffee?

Solve a real-world set theory problem involving 13 people who like tea, 12 people who like coffee, and 3 people who like neither. Learn how to find the number of people who like tea but not coffee using the principle of inclusion-exclusion. Suitable for students in Grades 6-8.

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