# Acceptance Rate

The mean number of students has changed, so how many students applied to a school?

## 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 thatÂ $338 \times 5 = 1690$ students were accepted in total over the five years.

So in $2011$, $1690-1300=390$ students were accepted.