Team A contain 7 boys and n-girls , Team B has 4 boys and 6 girls. If each boy of Team A plays one match with each boy of Team B and each girl of Team A plays one match with every girls of Team B then total number of matches are 52 . Find value of n

Answer

To solve the problem, we need to calculate the total number of matches played between the boys and girls of Team A and Team B, and set that equal to 52.

1. **Identify the number of boys and girls in each team:**
- Team A has 7 boys and \( n \) girls.
- Team B has 4 boys and 6 girls.

2. **Calculate the matches played by boys:**
Each boy from Team A plays one match with each boy from Team B.
- Number of matches played by boys = Number of boys in Team A × Number of boys in Team B
- This is calculated as:
\[ \text{Matches by boys} = 7 \times 4 = 28 \]

3. **Calculate the matches played by girls:**
Each girl from Team A plays one match with each girl from Team B.
- Number of matches played by girls = Number of girls in Team A × Number of girls in Team B
- This is calculated as:
\[ \text{Matches by girls} = n \times 6 \]

4. **Set up the equation for total matches:**
The total number of matches is the sum of matches played by boys and girls, which is given as 52.
- Therefore, we can write:
\[ 28 + 6n = 52 \]

5. **Solve for \( n \):**
- First, isolate \( 6n \):
\[ 6n = 52 - 28 \]
\[ 6n = 24 \]
- Now, divide both sides by 6:
\[ n = \frac{24}{6} = 4 \]

Thus, the value of \( n \) is **4**.