In a class of 36 people, there are 26 people who are members of the math team and the computer team. If we know, out of these 26 people, there are only 5 people who are both teams and a total of 14 people are computer members. In this case, how many people are there in the math team?

We can solve this problem using a Venn diagram or the principle of inclusion-exclusion. Here's how we break it down:

Let:
- \( M \) represent the number of people on the math team.
- \( C \) represent the number of people on the computer team.
- The total number of people in the class is 36.

### Step 1: Information from the problem
- \( C = 14 \) (Total number of people on the computer team).
- There are 26 people in total who are on either the math team, the computer team, or both.
- Out of these 26 people, 5 are on **both** the math team and the computer team.

### Step 2: Apply the principle of inclusion-exclusion
The formula for the union of two sets is:
\[
|M \cup C| = |M| + |C| - |M \cap C|
\]
Where:
- \( |M \cup C| = 26 \) (total number of people on the math team, computer team, or both),
- \( |C| = 14 \) (total number of people on the computer team),
- \( |M \cap C| = 5 \) (number of people on both teams).

Substitute the known values into the formula:
\[
26 = |M| + 14 - 5
\]
\[
26 = |M| + 9
\]
### Step 3: Solve for \( |M| \)
\[
|M| = 26 - 9
\]
\[
|M| = 17
\]

Thus, there are **17 people on the math team**.

Would you like any additional details or clarifications? Here are five related questions you can explore:

1. How many people are on only the math team?
2. How many people are only on the computer team?
3. How many people are in the class but are not on either team?
4. What is the probability that a randomly selected person from the class is on both teams?
5. Can we represent this scenario with a Venn diagram?

**Tip:** Using a Venn diagram can help visualize problems involving sets, especially in cases like this with overlapping groups.

Solve the math team problem using the principle of inclusion-exclusion. Given a class of 36 students, 26 are on either the math or computer teams, with 5 students on both teams. Find out how many students are on the math team. Detailed breakdown of steps and formulas included. Suitable for Grades 8-10.

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