Answer :
To solve this problem, we need to determine the combined average weight of all the students (both girls and boys) in the class. Here’s a step-by-step explanation of how to find it:
1. Determine the total weight of the girls:
- There are 18 girls, and each has an average weight of 60 kg.
- To find the total weight of the girls, multiply the number of girls by the average weight:
[tex]\[ \text{Total weight of girls} = 18 \times 60 = 1080 \text{ kg} \][/tex]
2. Determine the total weight of the boys:
- There are 32 boys, and each has an average weight of 62 kg.
- To find the total weight of the boys, multiply the number of boys by the average weight:
[tex]\[ \text{Total weight of boys} = 32 \times 62 = 1984 \text{ kg} \][/tex]
3. Calculate the total number of students:
- The total number of students is the sum of the number of girls and boys:
[tex]\[ \text{Total number of students} = 18 + 32 = 50 \][/tex]
4. Calculate the combined total weight of all the students:
- This is the sum of the total weight of the girls and the total weight of the boys:
[tex]\[ \text{Total weight} = 1080 \text{ kg} + 1984 \text{ kg} = 3064 \text{ kg} \][/tex]
5. Calculate the average weight of all the students:
- The average weight is the total weight divided by the total number of students:
[tex]\[ \text{Average weight} = \frac{\text{Total weight}}{\text{Total number of students}} = \frac{3064 \text{ kg}}{50} = 61.28 \text{ kg} \][/tex]
Putting it all together, we find that the average weight of all 50 students in the class is:
[tex]\[ \boxed{61.28 \text{ kg}} \][/tex]
Thus, the correct answer is [tex]\( \boxed{61.28} \)[/tex].
1. Determine the total weight of the girls:
- There are 18 girls, and each has an average weight of 60 kg.
- To find the total weight of the girls, multiply the number of girls by the average weight:
[tex]\[ \text{Total weight of girls} = 18 \times 60 = 1080 \text{ kg} \][/tex]
2. Determine the total weight of the boys:
- There are 32 boys, and each has an average weight of 62 kg.
- To find the total weight of the boys, multiply the number of boys by the average weight:
[tex]\[ \text{Total weight of boys} = 32 \times 62 = 1984 \text{ kg} \][/tex]
3. Calculate the total number of students:
- The total number of students is the sum of the number of girls and boys:
[tex]\[ \text{Total number of students} = 18 + 32 = 50 \][/tex]
4. Calculate the combined total weight of all the students:
- This is the sum of the total weight of the girls and the total weight of the boys:
[tex]\[ \text{Total weight} = 1080 \text{ kg} + 1984 \text{ kg} = 3064 \text{ kg} \][/tex]
5. Calculate the average weight of all the students:
- The average weight is the total weight divided by the total number of students:
[tex]\[ \text{Average weight} = \frac{\text{Total weight}}{\text{Total number of students}} = \frac{3064 \text{ kg}}{50} = 61.28 \text{ kg} \][/tex]
Putting it all together, we find that the average weight of all 50 students in the class is:
[tex]\[ \boxed{61.28 \text{ kg}} \][/tex]
Thus, the correct answer is [tex]\( \boxed{61.28} \)[/tex].
