40% of the students in the Math team are in the Robotics team, and
20% of the students in the Robotics team are in the Math team. There are 50 students in the
Robotics team. How many students are in both teams?

Let's denote the total number of students in the Math team as \( M \) and the number of students who are in both the Math and Robotics teams as \( x \).

We have two key pieces of information:

1. **40% of the Math team is in the Robotics team**:
   \[
   0.4M = x
   \]

2. **20% of the Robotics team is in the Math team**:
   \[
   0.2 \times 50 = x
   \]

Now, let's calculate \( x \) from the second equation:

\[
x = 0.2 \times 50 = 10
\]

So, \( x = 10 \). This means that 10 students are in both teams.

**Summary**: There are 10 students who are in both the Math and Robotics teams.

Would you like any further details or explanations?

Here are 5 related questions to consider:
1. If there are 100 students in the Math team, how many students are in the Robotics team?
2. What is the total number of students involved in either the Math or Robotics teams or both?
3. What percentage of the total students involved in the Robotics team are also in the Math team?
4. How many students are only in the Math team and not in the Robotics team?
5. How would the number of students in both teams change if the percentage of Robotics team members in the Math team increased to 30%?

**Tip**: When working with percentages in word problems, converting the percentages to decimals and setting up equations based on the relationships described is a very effective strategy.

Learn how to solve a problem involving percentages and overlapping sets. Given that 40% of the Math team is in the Robotics team and 20% of the Robotics team is in the Math team, find the number of students in both teams. This problem is suitable for high school students and covers concepts in percentages and set theory.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation