Acceptance Rate
The mean number of students has changed, so how many students applied to a school?
Age
14 to 16
Challenge level
Problem
The mean number of students accepted by a school in the four years 2007 to 2010 was 325.
The mean number of students accepted by the school in the five years 2007 to 2011 was 4% higher.
How many students did this school accept in 2011?
This problem is taken from the UKMT Mathematical Challenges.
Student Solutions
Over the first four years, on average $325$ students were accepted,
so a total of $325 \times 4 = 1300$ were accepted.
A 4% increase means that over the five year period, on average,
$325 \times 1.04=338$ students were accepted each year.
This means that $338 \times 5 = 1690$ students were accepted in total over the five years.
So in $2011$, $1690-1300=390$ students were accepted.