In a class of 100 students, the average weight is 30 kg. If the average weight of the girls is 24 kg and the average weight of the boys is 32 kg, how many girls are there in the class?

Introduction / Context:
This question is a standard example of weighted averages applied to a mixture of two groups, girls and boys, within a class. You are given the overall average weight and the subgroup averages, and you must find the size of one subgroup. The problem reinforces the idea that the combined average is a weighted average of subgroup averages based on their sizes.

Given Data / Assumptions:

• Total number of students = 100.
• Average weight of the whole class = 30 kg.
• Average weight of girls = 24 kg.
• Average weight of boys = 32 kg.
• Let the number of girls be G and the number of boys be B.
• We know G + B = 100.
• We must find G.

Concept / Approach:
Total weight of the class can be expressed in two ways. From the overall average, it is 100 * 30. From the subgroup averages, it is (G * 24) + (B * 32). Since these represent the same total, we can equate them. Also, B can be replaced by 100 - G. Solving the resulting equation yields the number of girls. This is a classic weighted average setup.

Step-by-Step Solution:
Step 1: Let the number of girls be G and the number of boys be B. Step 2: Then G + B = 100 ⇒ B = 100 - G. Step 3: Total weight of all students from overall average = 100 * 30 = 3000 kg. Step 4: Total weight from subgroup averages = 24G + 32B. Step 5: Substitute B = 100 - G: total weight = 24G + 32(100 - G). Step 6: Expand: 24G + 3200 - 32G = 3000. Step 7: Combine like terms: (24G - 32G) + 3200 = 3000 ⇒ -8G + 3200 = 3000. Step 8: Subtract 3200 from both sides: -8G = -200. Step 9: Divide by -8: G = (-200) / (-8) = 25. Step 10: Therefore, there are 25 girls in the class.

Verification / Alternative check:
If there are 25 girls, then there are 75 boys. Total weight of girls = 25 * 24 = 600 kg. Total weight of boys = 75 * 32 = 2400 kg. Combined total = 600 + 2400 = 3000 kg. Dividing 3000 by 100 students gives an overall average of 30 kg, which matches the given data. This confirms that G = 25 is correct.

Why Other Options Are Wrong:
If G = 26, then B = 74 and total weight becomes 26 * 24 + 74 * 32, which does not equal 3000. Similar mismatches occur for G = 27 or 28 or 30. Only G = 25 produces a total weight consistent with the stated overall average of 30 kg.

Common Pitfalls:
Some students attempt to average the subgroup averages directly, for example (24 + 32) / 2, which is incorrect because the numbers of girls and boys are not equal. Others may forget to multiply each average by the correct group size when computing total weight. Always remember that overall average is total divided by total count, and total is additive across groups.

Final Answer:
The class has 25 girls.