In a prep school, the average weight o f 30 girls in a class of 50 stu...
Problem:
In a prep school, the average weight of 30 girls in a class of 50 students is 16 kg, and that of the remaining students is 15.5 kg. What is the average weight of all the students in the class?
Solution:
To find the average weight of all the students in the class, we need to consider the total weight of all the students and divide it by the total number of students.
Step 1: Find the total weight of the 30 girls.
Since the average weight of the 30 girls is given as 16 kg, we can calculate the total weight of the 30 girls by multiplying the average weight by the number of girls.
Total weight of the 30 girls = 16 kg * 30 = 480 kg
Step 2: Find the total weight of the remaining students.
To find the total weight of the remaining students, we need to subtract the total weight of the 30 girls from the total weight of all the students.
Total weight of the remaining students = Total weight of all the students - Total weight of the 30 girls
Since the total number of students is given as 50, we can calculate the total weight of all the students by multiplying the average weight of the remaining students by the number of remaining students.
Total weight of the remaining students = 15.5 kg * (50 - 30) = 15.5 kg * 20 = 310 kg
Step 3: Find the total weight of all the students.
To find the total weight of all the students, we need to add the total weight of the 30 girls and the total weight of the remaining students.
Total weight of all the students = Total weight of the 30 girls + Total weight of the remaining students
Total weight of all the students = 480 kg + 310 kg = 790 kg
Step 4: Find the average weight of all the students.
To find the average weight of all the students, we need to divide the total weight of all the students by the total number of students.
Average weight of all the students = Total weight of all the students / Total number of students
Average weight of all the students = 790 kg / 50 = 15.8 kg
Therefore, the average weight of all the students in the class is 15.8 kg, which corresponds to option B.