# There were 50 students in the chess club. The membership increased by 10%. How many total students are now in the club?

Dec 9, 2016

There are now 55 total students in the club.

#### Explanation:

The formula for calculating the percentage change is

$p = \frac{N - O}{O} \cdot 100$ where $p$ is the percent change, $N$ is the New Value and $O$ is the Old Value. In this problem we are given the Old Value (50) and the percent change (10). We can substitute this into the formula and solve for $N$:

$10 = \frac{N - 50}{50} \cdot 100$

$\frac{50}{100} \cdot 10 = \frac{N - 50}{50} \cdot 100 \cdot \frac{50}{100}$

$\frac{500}{100} = \frac{\left(N - 50\right)}{\cancel{50}} \cdot \cancel{100} \cdot \frac{\cancel{50}}{\cancel{100}}$

$5 = N - 50$

$5 + 50 = N - 50 + 50$

$55 = N$