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To solve this problem, let’s identify and organize the information given:

1. **Total students** in the class: 35
2. **Students who like basketball**: 20
3. **Students who like soccer**: 22
4. We are asked to find **how many students like both basketball and soccer**.

### Step-by-Step Solution:

Let:
- \( B \) = Number of students who like basketball = 20
- \( S \) = Number of students who like soccer = 22
- \( T \) = Total number of students in the class = 35
- \( x \) = Number of students who like both sports

Using the principle of inclusion-exclusion:
\[
B + S - x = T
\]

Substitute the known values:
\[
20 + 22 - x = 35
\]

Solve for \( x \):
\[
42 - x = 35
\]
\[
x = 42 - 35
\]
\[
x = 7
\]

### Answer:
The number of students who like both basketball and soccer is **7**.

Would you like further details on this solution or have any additional questions?

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Here are 5 additional questions related to set problems:

1. How would you calculate the number of students who like only basketball?
2. How can you determine the number of students who like only soccer?
3. What if the total number of students was unknown; how could you solve for it?
4. Can you apply this inclusion-exclusion principle to three sets (e.g., students who like basketball, soccer, and volleyball)?
5. What if there was an overlap with another sport, how would that affect the calculation?

**Tip:** For problems involving overlapping groups, the inclusion-exclusion principle is often very helpful.

Each student in a class likes either basketball or soccer. If there are 35 students in the class, 20 students who like basketball, and 22 students who like soccer, how many students like both basketball and soccer?

Learn how to determine the number of students who like both basketball and soccer using the Inclusion-Exclusion Principle. With a total of 35 students in the class, 20 students who like basketball, and 22 who like soccer, find how many students enjoy both sports. Ideal for students in Grades 6-8.

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