In a class of 65 students there are 39 girls. The average weight of these girls is 60 kg and the average weight of the whole class is 64 kg. What is the average weight of the boys in the class?

Introduction / Context:
This question is another example of a weighted average and subgroup problem. The class is divided into girls and boys with different average weights, and the average weight of the entire class is also given. The goal is to use this information to determine the boys' average weight.

Given Data / Assumptions:

Total number of students = 65.
Number of girls = 39, so number of boys = 65 - 39 = 26.
Average weight of the girls = 60 kg.
Average weight of the whole class = 64 kg.
We must find the average weight of the boys, in kilograms.

Concept / Approach:
Average weight multiplied by the number of students gives total weight. We first compute the total weight of all 65 students using the class average. Next, we compute the total weight of the 39 girls using their average. Subtracting the girls' total weight from the class total gives the total weight of the 26 boys. Dividing this by 26 yields the average weight of the boys.

Step-by-Step Solution:
Step 1: Compute total weight of the full class. Total class weight = 64 * 65 = 4160 kg. Step 2: Compute total weight of the girls. Total girls' weight = 60 * 39 = 2340 kg. Step 3: Compute total weight of the boys. Total boys' weight = total class weight - total girls' weight. Total boys' weight = 4160 - 2340 = 1820 kg. Step 4: Compute average weight of the boys. Number of boys = 26. Average boys' weight = 1820 / 26 = 70 kg.

Verification / Alternative Check:
We can verify by recomputing the overall average. Girls contribute 2340 kg, boys contribute 1820 kg, giving a total of 4160 kg. Dividing by 65 students gives 4160 / 65 = 64 kg, which matches the given class average. This confirms that 70 kg is the consistent average for the boys.

Why Other Options Are Wrong:
66 kg or 68 kg would give a smaller total weight for the boys, which would pull the overall class average below 64 kg, contradicting the question.
69 kg would be slightly low and would still not produce the exact total required for a 64 kg class average when combined with the girls' total weight.

Common Pitfalls:
Some learners try to find the boys' average by simply taking a difference between the two averages (for example, 64 and 60) without considering the number of students in each subgroup. Others miscalculate totals or forget to use the correct counts of boys and girls. Always work with totals: class total, girls' total, then boys' total, and finally compute the boys' average from their total and count.

Final Answer:
The average weight of the boys in the class is 70 kg.