The mean age of a group of students is 15 years. When the age of a teacher, 45 years old, is added to the age of the students, the mean of their ages becomes 18 years. Find the number of the students in the group
A
9
B
7
C
42
D
15
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
Let the number of students = x
Total age of the students = 15x
Total age including age of the teacher = 15x + 45
Mean of their ages; (15x + 45)/(x + 1) = 18
15x + 45 = 18(x + 1)
15x + 45 = 18x + 18
18x - 15x = 45 - 18
3x = 27
x = 9
Source: Myschool Past Questions Archive (Record #8194)