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Let's break down the problem step by step using set theory principles:

### Given:
- Total readers \( = 300 \)
- Readers of both magazines \( A \) and \( B \) (denoted as \( A \cap B \)) = 92
- Total readers of magazine \( B \) (denoted as \( |B| \)) = 128

We are asked to solve two questions:

### a) How many read only magazine \( A \), if 128 people read magazine \( B \)?

Let:
- \( |A| \) be the total number of readers of magazine \( A \).
- \( A \cap B \) represents those who read both magazines, which is 92.
- Readers of only magazine \( A \) will be \( |A| - A \cap B \).

Since the total number of readers is 300, the number of people who read only \( A \), only \( B \), and both should sum up to 300.

The number of people who read only \( B \) is \( |B| - A \cap B = 128 - 92 = 36 \).

Thus, to find the number of people who read only \( A \), we need to compute:

\[
|A \text{ only}| = 300 - (A \cap B + B \text{ only}) = 300 - (92 + 36) = 300 - 128 = 172
\]

So, the number of people who read only magazine \( A \) is 172.

### b) How many read only magazine \( B \)?

This was already calculated as part of the process in part (a):

\[
B \text{ only} = 128 - 92 = 36
\]

### Final answers:
- a) 172 people read only magazine \( A \).
- b) 36 people read only magazine \( B \).

Would you like a more detailed explanation or have any questions about these steps? 

Here are some related questions:
1. How would the problem change if more people read both magazines?
2. How can we represent this problem visually using Venn diagrams?
3. What if the total number of readers were different—how would the equations adjust?
4. How can you verify the solution using the principle of inclusion-exclusion?
5. How do you handle such problems when more than two sets (magazines) are involved?

**Tip:** For set problems, drawing a Venn diagram can often help visualize the distribution of elements across sets.

De 300 lectores de la biblioteca municipal, 92 leen las revistas A y B.
a) ¿Cuántos leen solamente la revista A, si 128 son lectores de la revista B?
b) ¿Cuántos leen sólo la revista B?

Solve a set theory problem involving 300 readers of magazines A and B, with 92 reading both. Learn how to calculate how many people read only magazine A and only magazine B using basic set theory principles. Suitable for students in Grades 6-8.

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