In a class of 66 students there are 33 girls. The average weight of the girls is 61 kg and the average weight of the entire class is 66 kg. What is the average weight of the boys in the class?

Introduction / Context:
This question uses group averages to find the average weight of a subgroup. The class is divided into girls and boys, and we know the average weight of the girls and the average weight of the class as a whole. Using these, we can find the average weight of the boys.

Given Data / Assumptions:

• Total students in the class = 66.
• Number of girls = 33, so number of boys = 66 - 33 = 33.
• Average weight of girls = 61 kg.
• Average weight of the entire class = 66 kg.
• We must find the average weight of the boys.

Concept / Approach:
The approach is based on total weights. The total weight of the class equals the sum of total weights of girls and boys. First we compute the total weight of all students using the overall average. Then we compute the total weight of the girls using their average and count. Subtracting the girls total from the grand total gives the boys total, which we then divide by the number of boys to obtain their average weight.

Step-by-Step Solution:
Step 1: Total weight of the entire class = average * number of students = 66 * 66 = 4356 kg. Step 2: Total weight of girls = average girl weight * number of girls = 61 * 33 = 2013 kg. Step 3: Total weight of boys = grand total - girls total = 4356 - 2013 = 2343 kg. Step 4: Number of boys = 33. Step 5: Average weight of boys = 2343 / 33 = 71 kg.

Verification / Alternative check:
Check that the combined average is correct. Boys average 71 kg, girls average 61 kg and there are equal numbers of boys and girls. The overall average should be (71 + 61) / 2 = 132 / 2 = 66 kg, which matches the given overall average. This confirms that our calculations for the boys average are correct.

Why Other Options Are Wrong:
If the boys average were 72, 73 or 69, the overall average would no longer be 66 when combined with the girls average of 61 and equal group sizes. For example, if the boys averaged 72 kg, the combined average would be (72 + 61) / 2 = 66.5 kg, which contradicts the given data. Only 71 kg yields the correct overall mean.

Common Pitfalls:
A common error is to subtract the girls average from the class average directly, which does not produce the boys average when group sizes are equal or unequal. Another mistake is miscomputing the total or forgetting that there are 33 boys. Always work with totals and divide by the correct count when isolating a subgroup average.

Final Answer:
The average weight of the boys in the class is 71 kg.