Final answer:
To find the average weight of all 50 students, we calculate the total weight by multiplying the average weights of the girls and boys with their respective numbers and then divide the sum of these totals by the total number of students. The correct average weight of all students is approximately 59 kg.
Step-by-step explanation:
To find the average weight of all the students in the class, we first need to calculate the total weight of the girls and the total weight of the boys, and then combine these to find the total weight of the entire class. After that, we divide this total weight by the number of students in the class to get the average.
First, we calculate the total weight of the girls and the boys:
- Total weight of girls = average weight of a girl × number of girls = 56 kg × 18 = 1008 kg
- Total weight of boys = average weight of a boy × number of boys = 62 kg × 32 = 1984 kg
Next, we sum these totals to get the overall total weight of the class:
Total weight of the class = total weight of girls + total weight of boys = 1008 kg + 1984 kg = 2992 kg
Finally, we divide the total weight by the total number of students to find the average weight of the class:
Average weight of the class = total weight of the class ⁄ total number of students = 2992 kg ⁄ 50 = 59.84 kg
Since we can't have a fraction of a kilogram in the options given, we round this to the nearest whole number.
The correct answer is:
(a) 59 kg