The mean age of a group of students is 15 years. When the age of a teacher is 45years old is added to the ages of the students, the mean of their ages becomes 18 years. Find the number of students in the group.
9
7
42
15
$\begin{align} & \text{Let the number of students}=x \\ & \text{Mean age of the students}={{{\bar{x}}}_{students}}=15 \\ & \text{Teacher age }=45 \\ & \text{Mean age of teacher and students}={{{\bar{x}}}_{teacher+students}} \\ & {{{\bar{x}}}_{teacher+students}}=18 \\ & \text{Total ages of the students }=15x \\ & \text{Total ages of the students and teacher }=15x+45 \\ & \text{Mean age of students and teacher}={{{\bar{x}}}_{teacher+students}} \\ & {{{\bar{x}}}_{teacher+students}}=18=\frac{15x+45}{x+1} \\ & 15x+45=18(x+1) \\ & 15x+45=18x+18 \\ & 3x=27 \\ & x=9 \\ & \text{The numbers of students are 9} \\\end{align}$