Solving for the Number of Girls in a Class Using Weight Averages

Understanding the distribution of students in a class, especially based on their weight averages, is a practical application of mathematical problem-solving techniques. This solution involves setting up and solving a system of equations to find the number of girls in a class given certain weight averages and the total number of students.

Camodel Problem and Given Data

Let's consider a class of 200 students with a mean weight of 70 kg. The mean weight of the boys in the class is 80 kg, while the mean weight of the girls is 55 kg. We need to find the number of girls in the class.

Step 1: Set Up the Equations

Let x represent the number of boys and y represent the number of girls in the class. The total number of students is 200, so:

x y 200

The total weight of the boys is 8 kg and the total weight of the girls is 55y kg. The total weight of all students is 14000 kg (200 * 70 kg), so:

8 55y 14000

Step 2: Solve the Equations

First, solve the first equation for y in terms of x:

y 200 - x

Next, substitute y into the second equation:

8 55(200 - x) 14000

Simplify and solve for x:

8 11000 - 55x 14000

25x 3000

x 120

Now, find y using the expression y 200 - x:

y 200 - 120

y 80

Conclusion

The number of boys in the class is 120, and the number of girls is 80.

Revised Problem Example

Let's look at a similar problem but with different numbers to further illustrate the process:

Total Students and Average Weight

Total students in class 200

Average weight 70 kg

Total weight 200 * 70 kg 14000 kg

Let the Total Number of Boys B

Average weight of boys 80 kg

Total weight of boys 80B kg

Number of girls Total students - number of boys

Number of girls 200 - B

Average weight of girls 55 kg

Total weight of girls 55 * (200 - B) kg

Setting Up the Equation

Total weight Weight of boys Weight of girls

14000 80B 55 * (200 - B)

Simplify the equation and solve for B:

14000 80B 11000 - 55B

14000 25B 11000

3000 25B

B 120

Now, the number of girls 200 - B 80

No. of boys 120

No. of girls 80

Conclusion

By setting up and solving the equations, we can determine the number of girls in the class based on the mean weight of boys and girls and the total mean weight of the class members.