The mean age group of some students is 15years. When the age of a teacher, 45 years old, is added to the ages of the students, the mean of their ages become 18 years. Find the number of students in the group.
A
7
B
9
C
15
D
42
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
x \(\frac{\sum x}{N}\)
15 = \(\frac{\sum x }{N}\)
\(\sum x\) = 15N........(i)
y = \(\frac{\sum y}{Ny} = \frac{\sum x + 45}{N + 1}\)
\(\frac{18}{1} = \frac{15N + 45}{N + 1}\)
18(N + 1) = 15N + 45
18N + 18 = 15N + 45
18N - 15N = 45 - 18
3N = 27
N = \(\frac{27}{3}\)
= 9
Source: Myschool Past Questions Archive (Record #56862)