https://file.aiquickdraw.com/mathbot/file/1726766068372qoxrxt0e.jpg

The problem states:

- The average score of girls is 73.
- The average score of boys is 71.
- The average score of the whole class is 71.8.

We are to find the percentage of girls in the class.

Let:
- \( x \) be the percentage of girls in the class.
- \( 100 - x \) be the percentage of boys in the class.

The overall average score can be expressed as a weighted average of the girls' and boys' scores:

\[
71.8 = \frac{73x + 71(100 - x)}{100}
\]

Let's solve this equation for \( x \), the percentage of girls.The percentage of girls in the class is 40%.

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

Here are 5 related questions to expand your understanding:
1. How would the percentage change if the overall average score were higher?
2. What would the percentage of boys be based on this result?
3. Can you calculate the number of girls if there are 50 students in total?
4. How would the solution change if the average score of boys were different?
5. Can this method be used if the averages were given for three groups instead of two?

**Tip:** When dealing with averages, especially weighted averages, always consider the weights as proportional to the size of the groups involved.

In a class, the average score of girls in an examination is 73 and that of boys is 71. The average score of the whole class is 71.8. Find the percentage of girls.

Learn how to find the percentage of girls in a class using weighted averages. Given the average scores of girls and boys, and the overall average score, calculate the percentage of girls in this algebraic problem suitable for Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation