Calculating Combined Average Marks for Class X and Y

The problem asks us to find the overall average marks when we combine students from two different classes, Class X and Class Y. We are given the number of students and their average marks for each class.

Understanding the Concept: Weighted Average

When dealing with averages of different groups, we need to consider the 'weight' each group contributes. In this case, the weight is the number of students in each class. The formula for the combined average is:

$$ \text{Combined Average} = \frac{\text{Total marks of all students}}{\text{Total number of students}} $$

We can calculate the total marks for each class by multiplying the number of students by their respective average marks.

Step-by-Step Calculation

Step 1: Calculate Total Marks for Class X

Number of students in Class X = 45

Average marks of Class X = 30

Total marks for Class X = (Number of students in Class X) × (Average marks of Class X)

$$ \text{Total Marks}_X = 45 \times 30 $$

$$ \text{Total Marks}_X = 1350 $$

Step 2: Calculate Total Marks for Class Y

Number of students in Class Y = 35

Average marks of Class Y = 18

Total marks for Class Y = (Number of students in Class Y) × (Average marks of Class Y)

$$ \text{Total Marks}_Y = 35 \times 18 $$

$$ \text{Total Marks}_Y = 630 $$

Step 3: Calculate Total Marks for Both Classes Combined

Total marks for both classes = Total marks of Class X + Total marks of Class Y

$$ \text{Total Marks}_{\text{Combined}} = 1350 + 630 $$

$$ \text{Total Marks}_{\text{Combined}} = 1980 $$

Step 4: Calculate the Total Number of Students

Total number of students = Number of students in Class X + Number of students in Class Y

$$ \text{Total Students} = 45 + 35 $$

$$ \text{Total Students} = 80 $$

Step 5: Calculate the Combined Average Marks

Combined Average Marks = (Total marks of both classes) / (Total number of students)

$$ \text{Combined Average} = \frac{1980}{80} $$

To simplify the fraction, we can divide both the numerator and the denominator by 10:

$$ \text{Combined Average} = \frac{198}{8} $$

Now, we can perform the division:

$$ \text{Combined Average} = 24.75 $$

Summary of Results

Here's a quick summary:

The average marks of the students of both classes together is 24.75.