In a class of 39 students there are 26 girls. The average weight of the girls is 42 kg, and the average weight of the entire class is 48 kg. What is the average weight (in kilograms) of the boys in the class?

Introduction / Context:
This question is another example of finding the average of a subgroup when the averages of the full group and another subgroup are known. We need to find the average weight of boys given the number of boys and girls, the average weight of girls, and the average weight of the class.

Given Data / Assumptions:

• Total number of students = 39.
• Number of girls = 26.
• Number of boys = 39 - 26 = 13.
• Average weight of girls = 42 kg.
• Average weight of the entire class = 48 kg.
• We assume all weights are accurately measured in kilograms.

Concept / Approach:
Let the average weight of the boys be b kg. Then:

• Total weight of class = 48 * 39.
• Total weight of girls = 42 * 26.
• Total weight of boys = b * 13.

The total weight of the class is equal to the sum of total weights of girls and boys. Using this equality, we can solve for b.

Step-by-Step Solution:
Step 1: Compute total weight of the class. Total class weight = 48 * 39 = 1872 kg. Step 2: Compute total weight of girls. Total weight of girls = 42 * 26 = 1092 kg. Step 3: Compute total weight of boys. Total weight of boys = total class weight - total girls weight. Total weight of boys = 1872 - 1092 = 780 kg. Step 4: Compute average weight of boys. Number of boys = 13. Average weight of boys = 780 / 13 = 60 kg.

Verification / Alternative check:
Check the combined average: girls contribute 26 * 42 = 1092 kg, boys contribute 13 * 60 = 780 kg. Combined total = 1092 + 780 = 1872 kg. When divided by 39 students, 1872 / 39 = 48 kg, which matches the given class average. This confirms that the boys average of 60 kg is correct.

Why Other Options Are Wrong:
If the boys average were 54 kg, then boys total would be 13 * 54 = 702 kg, giving class total 1092 + 702 = 1794 kg and average 1794 / 39 ≈ 46, not 48 kg. For 66 kg, boys total becomes 858 kg, giving class average above 49 kg. For 62 kg, the average would again not match 48 kg. Only 60 kg yields the correct overall average.

Common Pitfalls:
Students may try to simply average 42 and 48 without considering the different numbers of boys and girls. Some may also miscalculate totals by forgetting to multiply by the number of students. Always remember that average = total / count, so when working with multiple groups, convert to totals first and then combine them carefully.

Final Answer:
The average weight of the boys in the class is 60 kilograms.