A generation ago, the graduating class at Manchester High School was 300 students. This year, it is 18% larger. What is the current size of the graduating class?

Jan 13, 2017

The size of the current graduating class is 354.

Explanation:

The formula for determining the rate of change is:

$p = \frac{N - O}{O} \cdot 100$

Where:

$p$ is the percentage of change - 18 in this case.
$N$ is the New Value - what we are solving for
$O$ is the Old Value - 300 for this problem.

Substituting and solving for $N$ gives:

$18 = \frac{N - 300}{300} \cdot 100$

$18 = \frac{N - 300}{3 \cdot 100} \cdot 100$

$18 = \frac{N - 300}{3 \cdot \textcolor{red}{\cancel{\textcolor{b l a c k}{100}}}} \cdot \textcolor{red}{\cancel{\textcolor{b l a c k}{100}}}$

$18 = \frac{N - 300}{3}$

$18 \cdot \textcolor{red}{3} = \frac{N - 300}{3} \cdot \textcolor{red}{3}$

$54 = \frac{N - 300}{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}}} \cdot \cancel{\textcolor{red}{3}}$

$54 = N - 300$

$54 + \textcolor{red}{300} = N - 300 + \textcolor{red}{300}$

$354 = N - 0$

$354 = N$

$N = 354$