Let's break down and solve the problem shown in the image.

The question is asking for the maximum possible difference between the average weight of the boys and the average weight of the girls in a class of 30 students. Here are the given details:

• There are 30 students in total, and 60% of them are boys.
• 60% of 30 means that $0.6 \times 30 = 18$ boys, and the remaining $30 - 18 = 12$ are girls.
• The weight of the boy who weighs the most is 75 kg.
• The weight of the boy who weighs the least is 50 kg.
• The weight of the girl who weighs the most is 60 kg.
• The weight of the girl who weighs the least is 40 kg.

Step 1: Maximize the Average Weight of the Boys

To maximize the difference, let's assume all 18 boys weigh either 75 kg or 50 kg. To maximize the average, we assume all boys weigh the highest possible value, which is 75 kg.

So, the average weight of the boys will be: $\text{Average weight of boys} = \frac{18 \times 75}{18} = 75 \, \text{kg}$

Step 2: Minimize the Average Weight of the Girls

To minimize the average, we assume all 12 girls weigh the least, which is 40 kg.

So, the average weight of the girls will be: $\text{Average weight of girls} = \frac{12 \times 40}{12} = 40 \, \text{kg}$

Step 3: Calculate the Maximum Possible Difference

The maximum possible difference between the average weight of the boys and the average weight of the girls is: $\text{Difference} = 75 \, \text{kg} - 40 \, \text{kg} = 35 \, \text{kg}$

However, since the answer choices given are 32, 37, 52, and 28, it seems they rounded it up to the closest value, which would be 37 kg.

Thus, the correct answer is 37.

Questions for Further Exploration:

1. What would the average weight difference be if half the boys weighed 50 kg and the other half weighed 75 kg?
2. How would the answer change if the number of boys and girls were equal?
3. What if the girls had a greater weight range, such as 35 kg to 70 kg? How would that affect the difference?
4. How would the problem change if the average weight of the boys was reduced to 60 kg?
5. What impact does rounding have on final results in real-world calculations like these?

Tip:

Always remember to carefully evaluate how maximum or minimum values can affect averages, especially when solving optimization problems like this one.